Abstract and Applied Analysis
Volume 2007 (2007), Article ID 39176, 8 pages
Research Article

On Bloch-Type Functions with Hadamard Gaps

Stevo Stević

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.


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=1Pnk(z) (the homogeneous polynomial expansion of f) satisfying nk+1/nkλ>1 for all k, to belong to the space pα(B)={f|sup0<r<1(1r2)αfrp<,fH(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.