Generalized Hilbert-Type operator in Weighted Bergman Spaces

Abstract

If f be an analytic function on the unit disk in the complex plane We consider the generalized Hilbert-type operators defined by (refer PDF for equation) where   and b are non-negative real numbers. In particular, for ,  becomes the Generalized Hilbert operator  and for , it becomes the classical Hilbert operator . We study these operators acting on weighted Bergman spaces  of analytic functions in Here we give conditions on the parameters  and  such that  is bounded on .