Operators and strongly exposed points in the ball of Bergman space

Abstract

We describe the boundedness of linear operators from the weighted Bergman spaces ,under some conditions on the weight function ,into a general Banach space by means of the growth conditions at the boundary of certain fractional derivatives of a single X-valued analytic function . And we find the multipliers of Hardy space into Bergman space when the regions are simply connected regions .We show that the only functions that can have the wandering property in Bergman space are the inner functions ,and we investigate which boundary points in the closed unit ball at the Bergman space are strongly exposed .