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2019 | OriginalPaper | Buchkapitel

2. Hardy Spaces with Variable Exponents

verfasst von : Víctor Almeida, Jorge J. Betancor, Estefanía Dalmasso, Lourdes Rodríguez-Mesa

Erschienen in: New Trends in Applied Harmonic Analysis, Volume 2

Verlag: Springer International Publishing

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Abstract

In this paper, we make a survey on some recent developments of the theory of Hardy spaces with variable exponents in different settings.

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Literatur
1.
Zurück zum Zitat E. Acerbi, G. Mingione, Regularity results for a class of functionals with non-standard growth. Arch. Ration. Mech. Anal. 156(2), 121–140 (2001)MathSciNetMATHCrossRef E. Acerbi, G. Mingione, Regularity results for a class of functionals with non-standard growth. Arch. Ration. Mech. Anal. 156(2), 121–140 (2001)MathSciNetMATHCrossRef
2.
Zurück zum Zitat V. Almeida, J.J. Betancor, A.J. Castro, L. Rodríguez-Mesa, Variable exponent Hardy spaces associated with discrete Laplacians on graphs. Sci. China Math. 62(1), 73–124 (2019)MathSciNetMATHCrossRef V. Almeida, J.J. Betancor, A.J. Castro, L. Rodríguez-Mesa, Variable exponent Hardy spaces associated with discrete Laplacians on graphs. Sci. China Math. 62(1), 73–124 (2019)MathSciNetMATHCrossRef
4.
Zurück zum Zitat V. Almeida, J.J. Betancor, L. Rodríguez-Mesa, Anisotropic Hardy-Lorentz spaces with variable exponents. Canad. J. Math. 69(6), 1219–1273 (2017)MathSciNetMATHCrossRef V. Almeida, J.J. Betancor, L. Rodríguez-Mesa, Anisotropic Hardy-Lorentz spaces with variable exponents. Canad. J. Math. 69(6), 1219–1273 (2017)MathSciNetMATHCrossRef
5.
Zurück zum Zitat S.N. Antontsev, J.F. Rodrigues, On stationary thermo-rheological viscous flows. Ann. Univ. Ferrara Sez. VII Sci. Mat. 52(1), 19–36 (2006)MathSciNetMATHCrossRef S.N. Antontsev, J.F. Rodrigues, On stationary thermo-rheological viscous flows. Ann. Univ. Ferrara Sez. VII Sci. Mat. 52(1), 19–36 (2006)MathSciNetMATHCrossRef
6.
Zurück zum Zitat P. Auscher, X.T. Duong, A. McIntosh, Boundedness of banach space valued singular integral and Hardy spaces. Unplublished Manuscript (2005) P. Auscher, X.T. Duong, A. McIntosh, Boundedness of banach space valued singular integral and Hardy spaces. Unplublished Manuscript (2005)
7.
Zurück zum Zitat P. Auscher, J.M.A. Martell, Weighted norm inequalities, off-diagonal estimates and elliptic operators. II. Off-diagonal estimates on spaces of homogeneous type. J. Evol. Equ. 7, 2, 265–316 (2007)MathSciNetMATHCrossRef P. Auscher, J.M.A. Martell, Weighted norm inequalities, off-diagonal estimates and elliptic operators. II. Off-diagonal estimates on spaces of homogeneous type. J. Evol. Equ. 7, 2, 265–316 (2007)MathSciNetMATHCrossRef
8.
Zurück zum Zitat P. Auscher, A. McIntosh, E. Russ, Hardy spaces of differential forms on Riemannian manifolds. J. Geom. Anal. 18(1), 192–248 (2008)MathSciNetMATHCrossRef P. Auscher, A. McIntosh, E. Russ, Hardy spaces of differential forms on Riemannian manifolds. J. Geom. Anal. 18(1), 192–248 (2008)MathSciNetMATHCrossRef
9.
Zurück zum Zitat M. Bownik, Anisotropic Hardy spaces and wavelets. Mem. Amer. Math. Soc. 164, 781, vi+122 (2003) M. Bownik, Anisotropic Hardy spaces and wavelets. Mem. Amer. Math. Soc. 164, 781, vi+122 (2003)
11.
Zurück zum Zitat J. Cao, D.-C. Chang, D. Yang, S. Yang, Weighted local Orlicz-Hardy spaces on domains and their applications in inhomogeneous Dirichlet and Neumann problems. Trans. Amer. Math. Soc. 365(9), 4729–4809 (2013)MathSciNetMATHCrossRef J. Cao, D.-C. Chang, D. Yang, S. Yang, Weighted local Orlicz-Hardy spaces on domains and their applications in inhomogeneous Dirichlet and Neumann problems. Trans. Amer. Math. Soc. 365(9), 4729–4809 (2013)MathSciNetMATHCrossRef
12.
Zurück zum Zitat J. Cao, S. Mayboroda, D. Yang, Local Hardy spaces associated with inhomogeneous higher order elliptic operators. Anal. Appl. (Singap.) 15(2), 137–224 (2017)MathSciNetMATHCrossRef J. Cao, S. Mayboroda, D. Yang, Local Hardy spaces associated with inhomogeneous higher order elliptic operators. Anal. Appl. (Singap.) 15(2), 137–224 (2017)MathSciNetMATHCrossRef
13.
Zurück zum Zitat A. Carbonaro, A. McIntosh, A.J. Morris, Local Hardy spaces of differential forms on Riemannian manifolds. J. Geom. Anal. 23(1), 106–169 (2013)MathSciNetMATHCrossRef A. Carbonaro, A. McIntosh, A.J. Morris, Local Hardy spaces of differential forms on Riemannian manifolds. J. Geom. Anal. 23(1), 106–169 (2013)MathSciNetMATHCrossRef
14.
Zurück zum Zitat Y. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math. 66(4), 1383–1406 (2006)MathSciNetMATHCrossRef Y. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math. 66(4), 1383–1406 (2006)MathSciNetMATHCrossRef
16.
Zurück zum Zitat D.V. Cruz-Uribe, A. Fiorenza, Variable Lebesgue Spaces: Foundations and Harmonic Analysis. Applied and Numerical Harmonic Analysis (Birkhäuser/Springer, Heidelberg, 2013)MATHCrossRef D.V. Cruz-Uribe, A. Fiorenza, Variable Lebesgue Spaces: Foundations and Harmonic Analysis. Applied and Numerical Harmonic Analysis (Birkhäuser/Springer, Heidelberg, 2013)MATHCrossRef
17.
Zurück zum Zitat D. Cruz-Uribe, A. Fiorenza, J.M. Martell, C. Pérez, The boundedness of classical operators on variable \(L^p\) spaces. Ann. Acad. Sci. Fenn. Math. 31(1), 239–264 (2006)MathSciNetMATH D. Cruz-Uribe, A. Fiorenza, J.M. Martell, C. Pérez, The boundedness of classical operators on variable \(L^p\) spaces. Ann. Acad. Sci. Fenn. Math. 31(1), 239–264 (2006)MathSciNetMATH
18.
Zurück zum Zitat D. Cruz-Uribe, A. Fiorenza, C.J. Neugebauer, The maximal function on variable \(L^p\) spaces. Ann. Acad. Sci. Fenn. Math. 28(1), 223–238 (2003)MathSciNetMATH D. Cruz-Uribe, A. Fiorenza, C.J. Neugebauer, The maximal function on variable \(L^p\) spaces. Ann. Acad. Sci. Fenn. Math. 28(1), 223–238 (2003)MathSciNetMATH
20.
Zurück zum Zitat D. Cruz-Uribe, L.-A.D. Wang, Extrapolation and weighted norm inequalities in the variable Lebesgue spaces. Trans. Amer. Math. Soc. 369(2), 1205–1235 (2017)MathSciNetMATHCrossRef D. Cruz-Uribe, L.-A.D. Wang, Extrapolation and weighted norm inequalities in the variable Lebesgue spaces. Trans. Amer. Math. Soc. 369(2), 1205–1235 (2017)MathSciNetMATHCrossRef
21.
Zurück zum Zitat G. Dafni, H. Yue, Some characterizations of local bmo and \(h^1\) on metric measure spaces. Anal. Math. Phys. 2(3), 285–318 (2012)MathSciNetMATHCrossRef G. Dafni, H. Yue, Some characterizations of local bmo and \(h^1\) on metric measure spaces. Anal. Math. Phys. 2(3), 285–318 (2012)MathSciNetMATHCrossRef
22.
Zurück zum Zitat L. Diening, Theoretical and numerical results for electrorheological fluids. Ph.D. thesis, Univ. Freiburg im Breisgau, Mathematische Fakultät, 156 p. (2002) L. Diening, Theoretical and numerical results for electrorheological fluids. Ph.D. thesis, Univ. Freiburg im Breisgau, Mathematische Fakultät, 156 p. (2002)
23.
Zurück zum Zitat L. Diening, P. Harjulehto, P. Hästö, M. Ružička, Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics, vol. 2017 (Springer, Heidelberg, 2011)MATHCrossRef L. Diening, P. Harjulehto, P. Hästö, M. Ružička, Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics, vol. 2017 (Springer, Heidelberg, 2011)MATHCrossRef
24.
Zurück zum Zitat L. Diening, Maximal function on generalized Lebesgue spaces \(L^{p(\cdot )}\). Math. Inequal. Appl. 7(2), 245–253 (2004)MathSciNetMATH L. Diening, Maximal function on generalized Lebesgue spaces \(L^{p(\cdot )}\). Math. Inequal. Appl. 7(2), 245–253 (2004)MathSciNetMATH
25.
Zurück zum Zitat L. Diening, P. Harjulehto, P. Hästö, Y. Mizuta, T. Shimomura, Maximal functions in variable exponent spaces: limiting cases of the exponent. Ann. Acad. Sci. Fenn. Math. 34(2), 503–522 (2009)MathSciNetMATH L. Diening, P. Harjulehto, P. Hästö, Y. Mizuta, T. Shimomura, Maximal functions in variable exponent spaces: limiting cases of the exponent. Ann. Acad. Sci. Fenn. Math. 34(2), 503–522 (2009)MathSciNetMATH
26.
Zurück zum Zitat L. Diening, P. Hästö, S. Roudenko, Function spaces of variable smoothness and integrability. J. Funct. Anal. 256(6), 1731–1768 (2009)MathSciNetMATHCrossRef L. Diening, P. Hästö, S. Roudenko, Function spaces of variable smoothness and integrability. J. Funct. Anal. 256(6), 1731–1768 (2009)MathSciNetMATHCrossRef
27.
Zurück zum Zitat L. Diening, M. Ružička, Calderón-Zygmund operators on generalized Lebesgue spaces \(L^{p(\cdot )}\) and problems related to fluid dynamics. J. Reine Angew. Math. 563, 197–220 (2003)MathSciNetMATH L. Diening, M. Ružička, Calderón-Zygmund operators on generalized Lebesgue spaces \(L^{p(\cdot )}\) and problems related to fluid dynamics. J. Reine Angew. Math. 563, 197–220 (2003)MathSciNetMATH
28.
Zurück zum Zitat X.T. Duong, L. Yan, Duality of Hardy and BMO spaces associated with operators with heat kernel bounds. J. Amer. Math. Soc. 18(4), 943–973 (2005) (electronic) X.T. Duong, L. Yan, Duality of Hardy and BMO spaces associated with operators with heat kernel bounds. J. Amer. Math. Soc. 18(4), 943–973 (2005) (electronic)
29.
Zurück zum Zitat P.L. Duren, B.W. Romberg, A.L. Shields, Linear functionals on \(H^{p}\) spaces with \(0<p<1\). J. Reine Angew. Math. 238, 32–60 (1969)MathSciNetMATH P.L. Duren, B.W. Romberg, A.L. Shields, Linear functionals on \(H^{p}\) spaces with \(0<p<1\). J. Reine Angew. Math. 238, 32–60 (1969)MathSciNetMATH
30.
32.
Zurück zum Zitat A. Gogatishvili, A. Danelia, T. Kopaliani, Local Hardy-Littlewood maximal operator in variable Lebesgue spaces. Banach J. Math. Anal. 8(2), 229–244 (2014)MathSciNetMATHCrossRef A. Gogatishvili, A. Danelia, T. Kopaliani, Local Hardy-Littlewood maximal operator in variable Lebesgue spaces. Banach J. Math. Anal. 8(2), 229–244 (2014)MathSciNetMATHCrossRef
34.
Zurück zum Zitat L. Grafakos, L. Liu, D. Yang, Radial maximal function characterizations for Hardy spaces on RD-spaces. Bull. Soc. Math. France 137(2), 225–251 (2009)MathSciNetMATHCrossRef L. Grafakos, L. Liu, D. Yang, Radial maximal function characterizations for Hardy spaces on RD-spaces. Bull. Soc. Math. France 137(2), 225–251 (2009)MathSciNetMATHCrossRef
35.
Zurück zum Zitat P. Harjulehto, P. Hästö, V. Latvala, O. Toivanen, Critical variable exponent functionals in image restoration. Appl. Math. Lett. 26(1), 56–60 (2013)MathSciNetMATHCrossRef P. Harjulehto, P. Hästö, V. Latvala, O. Toivanen, Critical variable exponent functionals in image restoration. Appl. Math. Lett. 26(1), 56–60 (2013)MathSciNetMATHCrossRef
37.
Zurück zum Zitat S. Hofmann, G. Lu, D. Mitrea, M. Mitrea, L. Yan, Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Memoirs of the Amer. Math. Soc. 214 (2011)MathSciNetMATHCrossRef S. Hofmann, G. Lu, D. Mitrea, M. Mitrea, L. Yan, Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates. Memoirs of the Amer. Math. Soc. 214 (2011)MathSciNetMATHCrossRef
38.
Zurück zum Zitat S. Hofmann, S. Mayboroda, Hardy and BMO spaces associated to divergence form elliptic operators. Math. Ann. 344(1), 37–116 (2009)MathSciNetMATHCrossRef S. Hofmann, S. Mayboroda, Hardy and BMO spaces associated to divergence form elliptic operators. Math. Ann. 344(1), 37–116 (2009)MathSciNetMATHCrossRef
39.
Zurück zum Zitat R. Jiang, D. Yang, D. Yang, Maximal function characterizations of Hardy spaces associated with magnetic Schrödinger operators. Forum Math. 24(3), 471–494 (2012)MathSciNetMATHCrossRef R. Jiang, D. Yang, D. Yang, Maximal function characterizations of Hardy spaces associated with magnetic Schrödinger operators. Forum Math. 24(3), 471–494 (2012)MathSciNetMATHCrossRef
40.
42.
Zurück zum Zitat O. Kováčik, J. Rákosník, On spaces \(L^{p(x)}\) and \(W^{k,p(x)}\). Czechoslovak Math. J. 41(4)(116), 592–618 (1991) O. Kováčik, J. Rákosník, On spaces \(L^{p(x)}\) and \(W^{k,p(x)}\). Czechoslovak Math. J. 41(4)(116), 592–618 (1991)
45.
Zurück zum Zitat F. Li, Z. Li, L. Pi, Variable exponent functionals in image restoration. Appl. Math. Comput. 216(3), 870–882 (2010)MathSciNetMATH F. Li, Z. Li, L. Pi, Variable exponent functionals in image restoration. Appl. Math. Comput. 216(3), 870–882 (2010)MathSciNetMATH
46.
Zurück zum Zitat J. Liu, D. Yang, W. Yuan, Anisotropic variable Hardy-Lorentz spaces and their real interpolation. J. Math. Anal. Appl. 456(1), 356–393 (2017)MathSciNetMATHCrossRef J. Liu, D. Yang, W. Yuan, Anisotropic variable Hardy-Lorentz spaces and their real interpolation. J. Math. Anal. Appl. 456(1), 356–393 (2017)MathSciNetMATHCrossRef
47.
Zurück zum Zitat G. Mauceri, M.A. Picardello, F. Ricci, A Hardy space associated with twisted convolution. Adv. in Math. 39(3), 270–288 (1981)MathSciNetMATHCrossRef G. Mauceri, M.A. Picardello, F. Ricci, A Hardy space associated with twisted convolution. Adv. in Math. 39(3), 270–288 (1981)MathSciNetMATHCrossRef
48.
Zurück zum Zitat E. Nakai, Y. Sawano, Hardy spaces with variable exponents and generalized Campanato spaces. J. Funct. Anal. 262(9), 3665–3748 (2012)MathSciNetMATHCrossRef E. Nakai, Y. Sawano, Hardy spaces with variable exponents and generalized Campanato spaces. J. Funct. Anal. 262(9), 3665–3748 (2012)MathSciNetMATHCrossRef
49.
Zurück zum Zitat H. Nakano, Modulared Semi-ordered Linear Spaces (Maruzen Co. Ltd., Tokyo, 1950)MATH H. Nakano, Modulared Semi-ordered Linear Spaces (Maruzen Co. Ltd., Tokyo, 1950)MATH
50.
Zurück zum Zitat A.S. Nekvinda, Hardy-Littlewood maximal operator on \(L^{p(x)}(\mathbb{R})\). Math. Inequal. Appl. 7(2), 255–265 (2004) A.S. Nekvinda, Hardy-Littlewood maximal operator on \(L^{p(x)}(\mathbb{R})\). Math. Inequal. Appl. 7(2), 255–265 (2004)
51.
52.
53.
Zurück zum Zitat L.S. Pick, M. Ružička, An example of a space \(L^{p(x)}\) on which the Hardy-Littlewood maximal operator is not bounded. Expo. Math. 19(4), 369–371 (2001) L.S. Pick, M. Ružička, An example of a space \(L^{p(x)}\) on which the Hardy-Littlewood maximal operator is not bounded. Expo. Math. 19(4), 369–371 (2001)
54.
Zurück zum Zitat K.R. Rajagopal, M. Ružička, On the modelling of electrorheological materials. Mech. Res. Commun. 23(4), 401–407 (1996)MATHCrossRef K.R. Rajagopal, M. Ružička, On the modelling of electrorheological materials. Mech. Res. Commun. 23(4), 401–407 (1996)MATHCrossRef
55.
Zurück zum Zitat M. Ružička, Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Mathematics, vol. 1748 (Springer, Berlin, 2000)MATHCrossRef M. Ružička, Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Mathematics, vol. 1748 (Springer, Berlin, 2000)MATHCrossRef
56.
Zurück zum Zitat Y. Sawano, Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operators. Int. Equ. Oper. Theory 77(1), 123–148 (2013)MathSciNetMATHCrossRef Y. Sawano, Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operators. Int. Equ. Oper. Theory 77(1), 123–148 (2013)MathSciNetMATHCrossRef
57.
Zurück zum Zitat I.I. Sharapudinov, The topology of the space \({\cal{L}}^{p(t)}([0,\,1])\). Mat. Zametki 26(4), 613–632, 655 (1979) I.I. Sharapudinov, The topology of the space \({\cal{L}}^{p(t)}([0,\,1])\). Mat. Zametki 26(4), 613–632, 655 (1979)
58.
Zurück zum Zitat L. Song, L. Yan, Maximal function characterization for Hardy spaces associated with nonnegative self-adjoint operators on spaces of homogeneous type. J. Evol. Equations. 18(1), 221–243 (2018)MathSciNetMATHCrossRef L. Song, L. Yan, Maximal function characterization for Hardy spaces associated with nonnegative self-adjoint operators on spaces of homogeneous type. J. Evol. Equations. 18(1), 221–243 (2018)MathSciNetMATHCrossRef
59.
Zurück zum Zitat L. Song, L. Yan, A maximal function characterization for Hardy spaces associated to nonnegative self-adjoint operators satisfying Gaussian estimates. Adv. Math. 287, 463–484 (2016)MathSciNetMATHCrossRef L. Song, L. Yan, A maximal function characterization for Hardy spaces associated to nonnegative self-adjoint operators satisfying Gaussian estimates. Adv. Math. 287, 463–484 (2016)MathSciNetMATHCrossRef
60.
Zurück zum Zitat E.M. Stein, Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals. Princeton Mathematical Series, vol. 43 (Princeton University Press, Princeton, NJ, 1993) E.M. Stein, Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals. Princeton Mathematical Series, vol. 43 (Princeton University Press, Princeton, NJ, 1993)
61.
Zurück zum Zitat E.M. Stein, G. Weiss, On the theory of harmonic functions of several variables. I. The theory of \(H^{p}\)-spaces. Acta Math. 103, 25–62 (1960)MathSciNetMATHCrossRef E.M. Stein, G. Weiss, On the theory of harmonic functions of several variables. I. The theory of \(H^{p}\)-spaces. Acta Math. 103, 25–62 (1960)MathSciNetMATHCrossRef
62.
Zurück zum Zitat J.-O. Strömberg, A. Torchinsky, Weighted Hardy Spaces. Lecture Notes in Mathematics, vol. 1381 (Springer, Berlin, 1989)MATHCrossRef J.-O. Strömberg, A. Torchinsky, Weighted Hardy Spaces. Lecture Notes in Mathematics, vol. 1381 (Springer, Berlin, 1989)MATHCrossRef
64.
Zurück zum Zitat H. Triebel, Theory of Function Spaces. Monographs in Mathematics, vol. 78 (Birkhäuser Verlag, Basel, 1983) H. Triebel, Theory of Function Spaces. Monographs in Mathematics, vol. 78 (Birkhäuser Verlag, Basel, 1983)
65.
Zurück zum Zitat A. Uchiyama, A maximal function characterization of \(H^{p}\) on the space of homogeneous type. Trans. Amer. Math. Soc. 262(2), 579–592 (1980)MathSciNetMATH A. Uchiyama, A maximal function characterization of \(H^{p}\) on the space of homogeneous type. Trans. Amer. Math. Soc. 262(2), 579–592 (1980)MathSciNetMATH
67.
Zurück zum Zitat A.S. Wineman, K.R. Rajagopal, On a constitutive theory for materials undergoing microstructural changes. Arch. Mech. (Arch. Mech. Stos.) 42(1), 53–75 (1990) A.S. Wineman, K.R. Rajagopal, On a constitutive theory for materials undergoing microstructural changes. Arch. Mech. (Arch. Mech. Stos.) 42(1), 53–75 (1990)
68.
Zurück zum Zitat L. Yan, Classes of Hardy spaces associated with operators, duality theorem and applications. Trans. Amer. Math. Soc. 360(8), 4383–4408 (2008)MathSciNetMATHCrossRef L. Yan, Classes of Hardy spaces associated with operators, duality theorem and applications. Trans. Amer. Math. Soc. 360(8), 4383–4408 (2008)MathSciNetMATHCrossRef
69.
Zurück zum Zitat D. Yang, J. Zhang, C. Zhuo, Variable Hardy spaces associated with operators satisfying Davies-Gaffney estimates. Proc. Edinburgh Math. Soc. 61(3), 759–810 (2018)MathSciNetMATHCrossRef D. Yang, J. Zhang, C. Zhuo, Variable Hardy spaces associated with operators satisfying Davies-Gaffney estimates. Proc. Edinburgh Math. Soc. 61(3), 759–810 (2018)MathSciNetMATHCrossRef
70.
Zurück zum Zitat D. Yang, S. Yang, Local Hardy spaces of Musielak-Orlicz type and their applications. Sci. China Math. 55(8), 1677–1720 (2012)MathSciNetMATHCrossRef D. Yang, S. Yang, Local Hardy spaces of Musielak-Orlicz type and their applications. Sci. China Math. 55(8), 1677–1720 (2012)MathSciNetMATHCrossRef
71.
Zurück zum Zitat D. Yang, C. Zhuo, Molecular characterizations and dualities of variable exponent Hardy spaces associated with operators. Ann. Acad. Sci. Fenn. Math. 41(1), 357–398 (2016)MathSciNetMATHCrossRef D. Yang, C. Zhuo, Molecular characterizations and dualities of variable exponent Hardy spaces associated with operators. Ann. Acad. Sci. Fenn. Math. 41(1), 357–398 (2016)MathSciNetMATHCrossRef
72.
Zurück zum Zitat D. Yang, C. Zhuo, E. Nakai, Characterizations of variable exponent Hardy spaces via Riesz transforms. Rev. Mat. Complut. 29(2), 245–270 (2016)MathSciNetMATHCrossRef D. Yang, C. Zhuo, E. Nakai, Characterizations of variable exponent Hardy spaces via Riesz transforms. Rev. Mat. Complut. 29(2), 245–270 (2016)MathSciNetMATHCrossRef
73.
Zurück zum Zitat X. Yan, D. Yang, W. Yuan, C. Zhuo, Variable weak Hardy spaces and their applications. J. Funct. Anal. 271(10), 2822–2887 (2016)MathSciNetMATHCrossRef X. Yan, D. Yang, W. Yuan, C. Zhuo, Variable weak Hardy spaces and their applications. J. Funct. Anal. 271(10), 2822–2887 (2016)MathSciNetMATHCrossRef
74.
Zurück zum Zitat V.V. Zhikov, Meyer-type estimates for solving the nonlinear Stokes system. Differ. Uravn. 33(1), 107–114, 143 (1997) V.V. Zhikov, Meyer-type estimates for solving the nonlinear Stokes system. Differ. Uravn. 33(1), 107–114, 143 (1997)
75.
Zurück zum Zitat C. Zhuo, Y. Sawano, D. Yang, Hardy spaces with variable exponents on RD-spaces and applications. Dissertationes Math. (Rozprawy Mat.) 520, 74 (2016)MathSciNetMATH C. Zhuo, Y. Sawano, D. Yang, Hardy spaces with variable exponents on RD-spaces and applications. Dissertationes Math. (Rozprawy Mat.) 520, 74 (2016)MathSciNetMATH
76.
Zurück zum Zitat C. Zhuo, D. Yang, Maximal function characterizations of variable Hardy spaces associated with non-negative self-adjoint operators satisfying Gaussian estimates. Nonlinear Anal. 141, 16–42 (2016)MathSciNetMATHCrossRef C. Zhuo, D. Yang, Maximal function characterizations of variable Hardy spaces associated with non-negative self-adjoint operators satisfying Gaussian estimates. Nonlinear Anal. 141, 16–42 (2016)MathSciNetMATHCrossRef
77.
Zurück zum Zitat C. Zhuo, D. Yang, Y. Liang, Intrinsic square function characterizations of Hardy spaces with variable exponents. Bull. Malays. Math. Sci. Soc. 39(4), 1541–1577 (2016)MathSciNetMATHCrossRef C. Zhuo, D. Yang, Y. Liang, Intrinsic square function characterizations of Hardy spaces with variable exponents. Bull. Malays. Math. Sci. Soc. 39(4), 1541–1577 (2016)MathSciNetMATHCrossRef
Metadaten
Titel
Hardy Spaces with Variable Exponents
verfasst von
Víctor Almeida
Jorge J. Betancor
Estefanía Dalmasso
Lourdes Rodríguez-Mesa
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-32353-0_2