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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.
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Abstract

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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

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