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Erschienen in:
Some Problems in Fourier Analysis and Approximation Theory Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Elementary Proofs of Embedding Theorems for Potential Spaces of Radial Functions

verfasst von : Pablo L. De Nápoli, Irene Drelichman

Erschienen in: Methods of Fourier Analysis and Approximation Theory

Verlag: Springer International Publishing

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Abstract

We present elementary proofs of weighted embedding theorems for radial potential spaces and some generalizations of Ni’s and Strauss’ inequalities in this setting.

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Vorheriges Kapitel Off-Diagonal and Pointwise Estimates for Compact Calderón-Zygmund Operators
Nächstes Kapitel On Leray’s Formula
Literatur
1.
C.O. Alves, G.M. Figueiredo, J.A. Santos, Strauss- and Lions-type results for a class of Orlicz-Sobolev spaces and applications. Topol. Method Nonlinear Anal. 44(2), 435–456 (2014)MathSciNet
2.
R. Adams, J.J.F. Fournier, Sobolev Spaces, 2nd edn. Pure and Applied Mathematics (Amsterdam), vol. 140 (Elsevier/Academic Press, Amsterdam, 2003)
3.
4.
5.
A.P. Calderón, Lebesgue Spaces of Differentiable Functions and Distributions. Proceedings of Symposia in Pure Mathematics, vol. V (American Mathematical Society, Providence, RI, 1961), pp. 33–49
6.
7.
P. D’Ancona, R. Luca, Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities with angular integrability. J. Math. Anal. Appl. 388, 1061–1079 (2012)MathSciNetCrossRefMATH
8.
L. De Carli, On the L p − L q norm of the Hankel transform and related operators. J. Math. Anal. Appl. 348, 366–382 (2008)MathSciNetCrossRefMATH
9.
D.G. de Figueiredo, E. Moreira dos Santos, O. Miyagaki, Sobolev spaces of symmetric functions and applications. J. Funct. Anal. 261:12, 3735–3770 (2011)
10.
11.
D.G. de Figueiredo, I. Peral, J. Rossi, The critical hyperbola for a hamiltonian elliptic system with weights. Annali di Matematica Pura ed Applicata Appl. 187, 531–545 (2008)MathSciNetCrossRefMATH
12.
P. De Nápoli, I. Drelichman, R. G. Durán, Radial solutions for hamiltonian elliptic systems with weights. Adv. Nonlinear Stud. 9:3, 579–594 (2009)
13.
P. De Nápoli, I. Drelichman, R.G. Durán, On weighted inequalities for fractional integrals of radial functions. Ill. J. Math. 55:2, 575–587 (2011)
14.
P. De Nápoli, I. Drelichman, Weighted convolution inequalities for radial functions. Ann. Mat. Pura Appl. (4) 194(1), 167–181 (2015). Doi: 10.1007/s10231-013-0370-6
15.
P. De Nápoli, I. Drelichman, N. Saintier, Weighted embedding theorems for radial Besov and Triebel-Lizorkin spaces, preprint 2014, arXiv:1406.0542
16.
G. Dinca, P. Jebelean, J. Mawhin, Variational and topological methods for Dirichlet problems with p-Laplacian. Portugaliae Mathematica 58:3, 339–378 (2001)
17.
E. Di Nezza, G. Palatucci, E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136:5, 521–573 (2012)
18.
19.
J. Duoandikoetxea, Fractional integrals on radial functions with applications to weighted inequalities. Ann. Mat. Pura Appl. 192(4), 553–568 (2013)MathSciNetCrossRefMATH
20.
L.C. Evans, Partial Differential Equations. Graduate Studies in Mathematics, vol. 19 (American Mathematical Society, Providence, RI, 1998)
21.
H. Hanche-Olsen, H. Holden, The Kolmogorov-Riesz compactness theorem. Expo. Math. 28:4, 385–394 (2010)
22.
D. Haroske, I. Piotrowska, Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis. Math. Nachr. 281(10), 1476–1494 (2008)MathSciNetCrossRefMATH
23.
D. Haroske, L. Skrzypczak, Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights. I. Rev. Mat. Complut. 21(1), 135–177 (2008)MathSciNetMATH
24.
D. Haroske, L. Skrzypczak, Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. General weights. Ann. Acad. Sci. Fenn. Math. 36(1), (2011), 111–138.MathSciNetCrossRefMATH
25.
26.
T. Kurokawa, On the relations between Bessel potential spaces and Riesz potential spaces. Potential Anal. 12(3), 299–323 (2000)MathSciNetCrossRefMATH
27.
28.
C. Martínez, M. Sanz, F. Periago, Distributional fractional powers of the Laplacean. Riesz potentials. Stud. Math. 135(3), 253–271 (1999)MathSciNetMATH
29.
M. Meyries, M. Veraar, Sharp embedding results for spaces of smooth functions with power weights. Stud. Math. 208(3), 257–293 (2012)MathSciNetCrossRefMATH
30.
M. Meyries, M. Veraar, Characterization of a class of embeddings for function spaces with Muckenhoupt weights. Arch. Math. 103, 435–449 (2014)MathSciNetCrossRefMATH
31.
32.
A. Nowak, K. Stempak, Potential operators associated with Hankel and Hankel-Dunkl transforms. J. Anal. Math. (to appear), arXiv: 1402.3399
33.
E. Nursultanov, S. Tikhonov, Weighted norm inequalities for convolution and riesz potential. Potential Anal. 42, 435–456 (2015). Doi: 10.1007/s11118-014-9440-7.MathSciNetCrossRefMATH
34.
35.
P. Rabinowitz, Minimax Methods in Criticalpoint Theory with Applications to Differential Equations. CBMS Regional Conference Series in Mathematics, vol. 65 (American Mathematical Society, RI, 1986)
36.
W. Rother, Some existence theorems for the equation − Δ u + K(x)u p = 0. Commun. Partial Differ. Eq. 15, 1461–1473 (1990)MathSciNetCrossRefMATH
37.
B.S. Rubin, One-dimensional representation, inversion and certain properties of Riesz potentials of radial functions (Russian). Math. Zametki 34(4), 521–533 (1983) [English translation: Math. Notes 34(3–4) 751–757 (1983)]
38.
B.S. Rubin, Fractional Integrals and Potentials. Monographs and Surveys in Pure and Applied Mathematics (Chapman and Hall/CRC, Boca Raton, 1996)
39.
G. Samko, Hypersingular Integrals and Their Applications, Series Analytical Methods and Special Functions (Taylor & Francis, London, 2002)
40.
S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives (Gordon and Breach Science, New York, 1983)MATH
41.
S. Secchi, On fractional Schrödinger equations in ℝ n without the Ambrosetti-Rabinowitz condition, preprint 2014, arXiv:1210.0755
42.
W. Sickel, L. Skrzypczak, Radial subspaces of Besov and Lizorkin-Triebel classes: extended Strauss lemma and compactness of embeddings. J. Fourier Anal. Appl. 6, 639–662 (2000)MathSciNetCrossRefMATH
43.
E.M. Stein, Singular Integrals and Differentiability Properties of Functions (Princeton University Press, Princeton, 1970)MATH
44.
E.M. Stein, The characterization of functions arising as potentials. Bull. Am. Math. Soc. 67(1), 1–163 (1961)MathSciNetCrossRef
45.
E.M. Stein, G. Weiss, Fractional integrals on n-dimensional Euclidean space. J. Math. Mech. 7, 503–514 (1958)MathSciNetMATH
46.
E.M. Stein, G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, Princeton, 1971)MATH
47.
48.
R.S. Strichartz, Multipliers on fractional Sobolev spaces. J. Math. Mech. 16, 1031–1060 (1967)MathSciNetMATH
49.
J. Su, Z. Wang, M. Willem, Weighted Sobolev imbedding with unbounded and decaying radial potentials. J. Differ. Eq. 238, 201–219 (2007)MathSciNetCrossRefMATH
50.
H. Triebel, Theory of Function Spaces II. Monographs in Mathematics, vol. 84 (Birkhäuser Verlag, Basel, 1992)
51.
Metadaten
Titel
Elementary Proofs of Embedding Theorems for Potential Spaces of Radial Functions
verfasst von
Pablo L. De Nápoli
Irene Drelichman
Copyright-Jahr
2016
Buch
Methods of Fourier Analysis and Approximation Theory

Print ISBN: 978-3-319-27465-2

Electronic ISBN: 978-3-319-27466-9

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-27466-9_8