Bloch-type functions with Hadamard gaps

摘要

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) = Sigma(infinity)(k-1)a(k)z(nk) where n(k+1)(k) >= lambda > 1 for all k is an element of N, to belong to the Bloch-type space B-u(D) = {f vertical bar sup(z is an element of D)mu(z)vertical bar f'(z)vertical bar < infinity, f is an element of H(D)}, as well as to the corresponding little Bloch- type space, under some conditions posed on the weight function mu. The main results are applied to a Bloch- type space of interest. (C) 2008 Elsevier Inc. All rights reserved.