On Bloch-Type Functions with Hadamard Gaps

Stevo Stevic

Abstract and Applied Analysis, 2007, vol. 2007, 1-8

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 ∈ ℕ , to belong to the space ℬ p α ( B ) = { f | sup 0 < r < 1 ( 1 − r 2 ) α \| ℛ 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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:039176

DOI: 10.1155/2007/39176

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