A class of integral operators from lebesgue spaces into harmonic bergman-besov or weighted bloch spaces

We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of Rn and characterize precisely those that are bounded from Lebesgue spaces Lp? into harmonic Bergman-Besov spaces bq?, weighted Bloch spaces b?? 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. © 2021, Hacettepe University. All rights reserved

A Class of Integral Operators Induced by Harmonic Bergman-Besov Kernels on Lebesgue Classes

We provide a full characterization in terms of the six parameters involved the boundedness of all standard weighted integral operators induced by harmonic Bergman-Besov kernels acting between different Lebesgue classes with standard weights on the unit ball of R-n. These operators in some sense generalize the harmonic Bergman-Besov projections. To obtain the necessity conditions, we use a technique that heavily depends on the precise inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball. This fruitful technique is new. It has been used first with holomorphic Bergman-Besov kernels by Kaptanoglu and Ureyen. Methods of the sufficiency proofs we employ are Schur tests or Holder or Minkowski type inequalities which also make use of estimates of Forelli-Rudin type integrals