Abstract and Applied Analysis
Volume 2007 (2007), Article ID 39176, 8 pages
doi:10.1155/2007/39176
Research Article
On Bloch-Type Functions with Hadamard Gaps
Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000, Serbia
Received 2 May 2007; Accepted 20 August 2007
Academic Editor: Simeon Reich
Copyright © 2007 Stevo Stević. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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∞Pnk(z) (the homogeneous polynomial expansion of f) satisfying nk+1/nk≥λ>1 for all k∈ℕ, to belong to the space ℬpα(B)={f|sup0<r<1(1−r2)α‖ℛfr‖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.