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arXiv · 1411.1648

Embedding theorems for Bergman spaces via harmonic analysis

José Ángel Peláez·Jouni Rättyä
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Abstract

Let $A^p_ω$ denote the Bergman space in the unit disc induced by a radial weight~$ω$ with the doubling property $\int_{r}^1ω(s)\,ds\le C\int_{\frac{1+r}{2}}^1ω(s)\,ds$. The positive Borel measures such that the differentiation operator of order $n\in\mathbb{N}\cup\{0\}$ is bounded from $A^p_ω$ into $L^q(μ)$ are characterized in terms of geometric conditions when $0<p,q<\infty$. En route to the proof a theory of tent spaces for weighted Bergman spaces is built.

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José Ángel Peláez, Jouni Rättyä. 2014-11-06. Embedding theorems for Bergman spaces via harmonic analysis. https://doi.org/10.1007/s00208-014-1108-5

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