Abstract and Applied Analysis
Volume 2007 (2007), Article ID 39176, 8 pages
doi:10.1155/2007/39176

On Bloch-type functions with Hadamard gaps

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.