Embedding theorems for Bergman spaces via harmonic analysis

Abstract

Let $A_{\omega }^p$ denote the Bergman space in the unit disc induced by a radial weight~$\omega$ with the doubling property ${\int }_r^1\omega (s)ds\le C{\int }_{\frac{1+r}{2}}^1\omega (s)ds$. The positive Borel measures such that the differentiation operator of order $n\in \mathbb{N}\cup \{0\}$ is bounded from $A_{\omega }^p$ into $L^q(\mu )$ 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.

appears in Mathematische Annalen 2014

Cited by in corpus (17)

• Small weighted Bergman spaces
• Zero sequences, factorization and sampling measures for weighted Bergman spaces
• Duality of holomorphic Hardy type tent spaces
• Compact Differences of Weighted Composition Operators
• Weighted norm inequalities for derivatives on Bergman spaces
• Volterra type integration operators from Bergman spaces to Hardy spaces
• Radial averaging operator acting on Bergman and Lebesgue spaces
• Tent Carleson measures for Hardy spaces
• Essential norms and weak compactness of integral operators between weighted Bergman spaces
• Interpolation and Sampling in Analytic Tent Spaces
• Embedding Theorem For Weighted Hardy Spaces into Lebesgue Spaces
• Carleson measures and Toeplitz operators on small Bergman spaces on the ball
• Generalized weighted composition operators on Bergman spaces induced by doubling weights
• Characterizations for inner functions in certain function spaces
• Difference of composition operators on weight Bergman spaces with doubling weight
• Berezin transform and Toeplitz operators on weighted Bergman spaces induced by regular weights
• Characterization of forward, vanishing, and reverse Bergman Carleson measures using sparse domination