Singular Integral Operators with Bergman-Besov Kernels on the Ball

Abstract

We completely characterize in terms of the six parameters involved the boundedness of all standard weighted integral operators induced by Bergman-Besov kernels acting between different Lebesgue classes with standard weights on the unit ball of CN. The integral operators generalize the Bergman-Besov projections. To find the necessary conditions for boundedness, we employ a new versatile method that depends on precise imbedding and inclusion relations among various holomorphic function spaces. The sufficiency proofs are by Schur tests or integral inequalities.