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 ${\mathbb{R}}^n$ and characterize precisely those that are bounded from Lebesgue spaces $L_{\alpha }^p$ into Harmonic Bergman-Besov $b_{\beta }^q$ or weighted Bloch Spaces $b_{\beta }^{\mathrm{\infty }}$, for $1\le p\le \mathrm{\infty }$, $1\le q<\mathrm{\infty }$ and $\alpha ,\beta \in \mathbb{R}$. These operators can be viewed as generalizations of the harmonic Bergman-Besov projections. Also, our results remove the disturbing conditions $\beta >-1$ when $q<\mathrm{\infty }$ and $\beta \ge 0$ when $q=\mathrm{\infty }$ of Do\u{g}an (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.