Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Bloch-type functions with Hadamard gaps
Journal: Applied Mathematics and Computation
Volume: 208
Issue: 2
First page: 416
Last page: 422
Issue Date: 15-Feb-2009
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2008.12.010
We give a sufficient and a necessary condition for an analytic function f on the unit disc D with Hadamard gaps, that is, for f (z) = ∑k = 1∞ ak znk where nk + 1 / nk ≥ λ > 1 for all k ∈ N, to belong to the Bloch-type space Bμ (D) = fenced(f | supz ∈ D μ (z) | f′ (z) | < ∞, f ∈ H (D)), as well as to the corresponding little Bloch-type space, under some conditions posed on the weight function μ. The main results are applied to a Bloch-type space of interest.
Keywords: Analytic function | Bloch-type space | Hadamard gap | Unit disk
Publisher: Elsevier

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