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 $\mathbb{R}^{n}$ and characterize precisely those that are bounded from Lebesgue spaces $L^{p}_{\alpha}$ into Harmonic Bergman-Besov $b^{q}_{\beta}$ or weighted Bloch Spaces $b^{\infty}_{\beta} $, for $1\leq p\leq\infty$, $1\leq q -1$ when $q<\infty$ and $\beta\geq 0$ when $q=\infty$ of Dogan (A Class of Integral Operators Induced by Harmonic Bergman-Besov kernels on Lebesgue Classes, preprint, 2020) by mapping the operators into these spaces instead of the Lebesgue classes.