Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-24T14:13:09.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Coefficient Inequalities for Lp-Valued Analytic Functions

Published online by Cambridge University Press:  20 November 2018

Lawrence A. Harris
Lawrence A. Harris*
Affiliation:
Department of Mathematics, University of Kentucky Lexington, Kentucky 40506
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.

A Hausdorff-Young theorem is given for Lp-valued analytic functions on the open unit disc and estimates on such functions and their derivatives are deduced.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 3 , 01 September 1981 , pp. 347 - 350
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Bromwich, T. J., Theory of Infinite Series, Macmillan, 2nd ed., London 1926.Google Scholar
2. Dunford, N. and Schwartz, J. T., Linear Operators, Interscience, New York, pt. I, 1958.Google Scholar
3. Duren, P. L., Theory of Hp Spaces, Academic Press, New York, 1970.Google Scholar
4. Hardy, G. H., Littlewood, J. E. and Polya, G., Inequalities, Cambridge University Press, London, 1934.Google Scholar
5. Harris, L., Bounds on the derivatives of holomorphic functions of vectors, Proc. Colloq. Analysis, Rio de Janeiro, 1972, 145-163, Nachbin, L., Ed., Act. Sci. et Ind. Paris: Hermann, 1975.Google Scholar
6. Hayden, T. and Wells, J., On the extension of Lipschitz-Hôlder maps of order a, J. Math. Anal. Appl. 33 (1971), 627-640.Google Scholar
7. Hille, E. and Phillips, R. S., Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ. 31, Providence, 1957.Google Scholar
8. Kestelman, H., Modern Theories of Integration, Oxford University Press, London 1937.Google Scholar
9. Renaud, A., Quelques propriétés des applications analytiques d'une boule de dimension infinie dans une autre, Bull. Sci. Math. 97 (1973), 129-159.Google Scholar
10. Titchmarsh, E. C., The Theory of Functions, Oxford University Press, 2nded., London 1939.Google Scholar
11. Williams, L. R. and Wells, J. H., Lp inequalities, J. Math. Anal. Appl. 64 (1978), 518-529.Google Scholar