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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

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

Ömer Faruk DOĞAN
Pages
811–820
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These operators can be viewed as generalizations of the harmonic Bergman-Besov projections.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact:These operators can be viewed as generalizations of the harmonic Bergman-Besov projections.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:integral operator · harmonic Bergman-Besov kernel · harmonic Bergman-Besov space

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.

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Cite This Article

DOĞAN, Ö. F. (2022). A class of integral operators from Lebesgue spaces into harmonic Bergman-Besov or weighted Bloch spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 811–820. https://ajindex.com/articles/529516

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