A class of integral operators from Lebesgue spaces into harmonic Bergman-Besov or weighted Bloch spaces

Abstract

We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of R n and characterize precisely those that are bounded from Lebesgue spaces L p α into harmonic Bergman-Besov spaces b q β , weighted Bloch spaces b ∞ β or the space of bounded harmonic functions h ∞ , allowing the exponents to be different. These operators can be viewed as generalizations of the harmonic Bergman-Besov projections.