Abstract and Applied Analysis

On Bloch-Type Functions with Hadamard Gaps

Stevo Stević

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Abstract

We give some sufficient and necessary conditions for an analytic function f on the unit ball B with Hadamard gaps, that is, for f ( z ) = k = 1 P n k ( z ) (the homogeneous polynomial expansion of f ) satisfying n k + 1 / n k λ > 1 for all k , to belong to the space p α ( B ) = { f | sup 0 < r < 1 ( 1 r 2 ) α \| f r \| p < , f H ( B ) } , p = 1 , 2 , as well as to the corresponding little space. A remark on analytic functions with Hadamard gaps on mixed norm space on the unit disk is also given.

Article information

Source
Abstr. Appl. Anal., Volume 2007 (2007), Article ID 39176, 8 pages.

Dates
First available in Project Euclid: 27 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1204126602

Digital Object Identifier
doi:10.1155/2007/39176

Mathematical Reviews number (MathSciNet)
MR2365811

Zentralblatt MATH identifier
1157.32301

Citation

Stević, Stevo. On Bloch-Type Functions with Hadamard Gaps. Abstr. Appl. Anal. 2007 (2007), Article ID 39176, 8 pages. doi:10.1155/2007/39176. https://projecteuclid.org/euclid.aaa/1204126602


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