Weak invertibility and factorization in certain spaces of analytic functions

9.5.

WEAK INVERTIBILITY AND FACTORIZATION IN CERTAIN SPACES OF

ANALYTIC FUNCTIONS*

is called a symmetric measure if ~ has the form ~(~,@)=(2X)-'~Y(~)d~ A measure ~ on where w is a finite, positive Borel measure on [0, I], having no mass at 0, and such that and any p, 0 < p < ~, v([r, I]) > 0 for all 0 ~ r < 1. For any function f analytic in ~ we define the generalized mean

0 ~< r