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 ∞ P nk (z) (the homogeneous polynomial expansion of f) satisfying n k+1 / nk <λ>1 for all k∈, to belong to the space ℬpα (B)={ f| sup 0<r<1 ( 1- r 2) α \| fr \|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.