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 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

References

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