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Weighted Subspaces of Hardy Spaces

Published online by Cambridge University Press:  20 November 2018

Hong Oh Kim  and
Ern Geun Kwon
Hong Oh Kim
Affiliation:
Korea Advanced Institute of Science and Technology, Seoul, Korea
Ern Geun Kwon
Affiliation:
Korea Advanced Institute of Science and Technology, Seoul, Korea
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A function f in Hp on the unit disc U of the complex plane has the uniform growth

We consider in this paper a subspace of Hp with better uniform growth

For the previous results on see [5, 6, 7]. We start with proving an inequality on Hp which is related to the Hardy-Stein identity (Theorem 2.1) in Section 2. This is applied in the subsequent section to prove some space imbedding theorems related to (Theorems 3.1 and 3.5). These theorems have some known theorems as their corollaries. Finally we prove some coefficient relations on in the last section.

The authors wish to thank Professor Patrick Ahern for the helpful conversations during his visit to Korea. Actually he suggested to the first author the possibility of Theorem 2.1 some years ago.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 5 , 01 October 1988 , pp. 1074 - 1083
Copyright
Copyright © Canadian Mathematical Society 1988

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