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arXiv · 2005.05314

A class of Integral Operators from Lebesgue spaces into Harmonic Bergman-Besov or Weighted Bloch Spaces

Ömer Faruk Doğan
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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 $1\leq p\leq\infty$, $1\leq q< \infty$ 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 $q<\infty$ and $\beta\geq 0$ when $q=\infty$ 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.

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Ömer Faruk Doğan. 2020-05-10. A class of Integral Operators from Lebesgue spaces into Harmonic Bergman-Besov or Weighted Bloch Spaces. https://arxiv.org/abs/2005.05314

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