Lipschitz type inequality in weighted Bloch space Cal B_q

Abstract

Let B be the open unit ball with center 0 in the complex space {Bbb C}^n.For each q>0, Cal B_q consists of holomorphic functionsf:B rightarrow Bbb C which satisfysup_{z in B} (1 - parallel z parallel^2)^q parallel{bigtriangledown} f(z) parallel < infty .In this paper, we will show that functions inweighted Bloch spaces Cal B_q (0 < q < 1) satifies thefollowing Lipschitz type result for Bergman metric beta:vert f(z) - f(w) vert < C beta(z, w)for some constant C.