Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-29T23:39:16.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Hardy-Littlewood-Sobolev Theorems of Fractional Integration on Herz-Type Spaces and its Applications

Published online by Cambridge University Press:  20 November 2018

Shanzhen Lu  and
Dachun Yang
Shanzhen Lu
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing100875, R R. China e-mail: lusz@sun.ihep.ac.cn
Dachun Yang
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing100875, R R. China e-mail: lusz@sun.ihep.ac.cn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, the authors first establish the Hardy-Littlewood-Sobolev theorems of fractional integration on the Herz spaces and Herz-type Hardy spaces. Then the authors give some applications of these theorems to the Laplacian and wave equations.

Keywords

42B2035J05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 2 , 01 April 1996 , pp. 363 - 380
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Baernstein, A., II and Sawyer, E.T., ), Mem. Amer. Math. Soc. 53 (1985).Google Scholar
2. Chen, Y.Z. and Lau, K.S., On some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), 255–278.Google Scholar
3. Coiftnan, R., Lions, R. L., Meyer, Y. and Semmes, S., Compensated compactness and Hardy spaces, J. Math. Pures Appl. (9) 72 (1993), 247–286.Google Scholar
4. Fefferman, C. and Stein, E.M., IF spaces of several variables, Acta Math. 129 (1972), 137–193.Google Scholar
5. García-Cuerva, J., Hardy spaces and Beurling algebras, J. London Math. Soc.(2) 39 (1989), 499–513.Google Scholar
6. Lu, S.Z. and Soria, F., Weighted inequalities for a class of operators related to the disc multiplier, preprint.Google Scholar
7. Lu, S.Z. and Yang, D.C., N and its applications, Sci. China Ser. A 2 (1995), 147–158.Google Scholar
8. Lu, S.Z. and Yang, D.C., The weighted Herz-type Hardy spaces and its applications, Sci. China Ser. A 6 (1995), 662–673.Google Scholar
9. Lu, S.Z. and Yang, D.C., Regularity of non-linear quantities in compensated compactness theory on Herztype spaces, preprint.Google Scholar
10. Stein, E.M., Singular integrals and differentiability properties of functions, Princeton Univ. Press, N. J., 1970.Google Scholar
11. Stein, E.M. and Weiss, G., Fractional integrals on n-dimensional Euclidean space, J. Math. Mech. 7 (1958), 503–514.Google Scholar
12. Taibleson, M.H. and Weiss, G., The molecular characterization of certain Hardy spaces, Asterisque 77 (1980), 67–149.Google Scholar