On the Forelli–Rudin Projection Theorem

Abstract

Abstract. Motivated by the Forelli-Rudin projection theorem we give in this paper a criterion for boundedness of an integral operator on weighted Lebesgue spaces in the interval (0, 1). We also calculate the precise norm of this integral operator. This is the content of the first part of the paper. In the second part, as applications, we give some results concerning the Bergman projection and the Berezin transform. We derive a generalization of the Dostanić result on the norm of the Berezin transform acting on Lebesgue spaces over the unit ball in C n .

Boundedness of a family of Hilbert-type operators and its Bergman-type analogue

“…The above lemma has a very simple formulation when p = q = 1, and the exact norm of the operator is also obtained (see [4]).…”

On the norm of the weighted Berezin transform

“…It should be pointed out that the Berezin transform is an analogue of the Poisson transform in Bergman space theory, see [11]. Recent results concerning the norm of the Berezin transform on L p (B n ) can be found in Dostanić's and Marković's papers [2] and [4].…”