Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T22:40:04.075Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the coefficients of mixed normed spaces

Published online by Cambridge University Press:  17 April 2009

E. G. Kwon
E. G. Kwon
Affiliation:
Department of Mathematics Education, Andong National University, Andong Kyungpook 660, Korea.
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.

For 0 < P,q < ∞, α> −1, Ap,q,α denotes the space of all holomorphic functions in the unit disc satisfying

where

In this paper, we find a sufficient condition for the multipliers from AP,q,α into ls, 1 ≤ s ≤ ∞, 1 ≤ q ≤ 2, which interpolates the results of Patrick Ahern and Miroljub Jevtic. As a corollary, we can calculate

for q′ ≤ s ≤ ∞, 1/q + 1/q′ = 1. Also, we can find a sharp coefficient condition for HP functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 2 , April 1986 , pp. 253 - 260
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Ahern, P. and Jevtic, M., “Duality and multipliers for mixed norm spaces”, Michigan Math. J. 30 (1983), 53–63.Google Scholar
[2]Anderson, J. M. and Shields, A. L., “Coefficient multipliers of Bloch functions”, Trans. Amer. Math. Soc. 224 (1976), 255–265.Google Scholar
[3]Duren, P. L., Theory of HP spaces, (Academic Press, New York, 1970).Google Scholar
[4]Holland, F. and Twomey, J. B., “Conditions for membership of Hardy spaces”, Aspect of contemporary analysis, (Academic Press, London 1980), 425–433.Google Scholar
[5]Kellog, C. N., “An extension of the Hausdorff-young theorem” Michigan Math. J. 18 (1971), 121–127.Google Scholar
[6]Mateljevuic, M. and Pavlovic, M., “LP-behaviour of power series with positive coefficients and Hardy spaces”, Proc. Amer. Math. Soc. 87 (1983), 309–316.Google Scholar