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

Authors : Ömer Faruk DOĞAN

Pages : 811-820

Doi:10.15672/hujms.768123

View : 27 | Download : 8

Publication Date : 2021-06-07

Article Type : Research Paper

Abstract :We consider a class of two-parameter weighted integral operators induced by harmonic Bergman-Besov kernels on the unit ball of $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into harmonic Bergman-Besov spaces $b^{q}_{\beta}$, weighted Bloch spaces $b^{\infty}_{\beta} $ or the space of bounded harmonic functions $h^{\infty}$, allowing the exponents to be different. These operators can be viewed as generalizations of the harmonic Bergman-Besov projections.
Keywords : integral operator, harmonic Bergman Besov kernel, harmonic Bergman Besov space, weighted harmonic Bloch space, harmonic Bergman Besov projection