Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-19T10:23:44.221Z Has data issue: false hasContentIssue false
  • English
  • Français

Mean Oscillation and Besov Spaces

Published online by Cambridge University Press:  20 November 2018

Jose R. Dorronsoro
Jose R. Dorronsoro*
Affiliation:
Washington UniversitySt. Louis, Mi, U.S.A. Universidad AutónomaMadrid, Spain
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.

The homogeneous Besov-Lipschitz spaces, usually defined by difference operators or Fourier transform, are studied in terms of mean oscillation, and several equivalent characterisations are given.

Keywords

46E3526A16
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 474 - 480
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Campanato, S., Propheta di una famiglia di spazi funzionali, Ann. Scuola Norm. Sup. Pisa 18 (1964), pp. 137–160.Google Scholar
2. Greenwald, H., Homogeneous Lipschitz spaces and mean oscillation, to appear in Pacif. J. of Math.Google Scholar
3. Janson, S., Taibleson, M. and Weiss, G., Elementary characterizations of Morrey-Campanato spaces, to appear in Pacif. J. of Math.Google Scholar
4. Johnen, H. and Scherer, K., On the equivalence of the K functional and moduli of continuity and some applications, Lecture Notes in Math. Springer-Verlag, 571, (1977), pp. 119–140.Google Scholar
5. Krantz, S.G., Geometric Lipschitz spaces and applications to complex function theory and nilpotent groups, J. Funct. Anal. 34, (1979), pp. 456–471.Google Scholar
6. Meyers, N.G., Mean oscillation over cubes and Holder continuity, Proc. Amer. Math. Soc. 15, (1964), pp. 717–721.Google Scholar
7. Nagel, A. and Stein, E.M., Lectures on pseudodifferential operators, Math. Notes 24, Princeton Univ. Press, 1979.Google Scholar
8. Peetre, J., New thoughts on Besov spaces, Duke University Mathematics Series 1, 1976.Google Scholar
9. Ricci, F. and Taibleson, M., Boundary values of harmonic functions on mixed norm spaces and their atomic structure, to appear in Ann. Scuola Norm. Sup. Pisa.Google Scholar
10. Stein, E.M., Singular integrals and differentiability properties of functions, Princeton Math. Series, Princeton University Press, 1970.Google Scholar