Carleson measures for weighted Bergman--Zygmund spaces

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Veröffentlicht in:	arXiv.org 2024-05
Hauptverfasser:	Cho, Hong Rae, Koo, Hyungwoon, Young Joo Lee, Pennanen, Atte, Rättyä, Jouni, Wu, Fanglei
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Schlagworte:	Analytic functions Operators (mathematics)
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For an integrable radial function $\omega$ on $\mathbb{D}$, the corresponding weighted Bergman-Zygmund space $A_{\omega, \Psi}^{p}$ is the set of all analytic functions in $L_{\mu, \Psi}^{p}$ with $d\mu=\omega\,dA$. The purpose of the paper is to characterize bounded (and compact) embeddings $A_{\omega,\Psi}^{p}\subset L_{\mu, \Phi}^{q}$, when $0<p\le q<\infty$, the functions $\Psi$ and $\Phi$ are essential monotonic, and $\Psi,\Phi,\omega$ satisfy certain doubling properties. The tools developed on the way to the main results are applied to characterize bounded and compact integral operators acting from $A^p_{\omega,\Psi}$ to $A^q_{\nu,\Phi}$, provided $\nu$ admits the same doubling property as $\omega$.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Analytic functions ; Operators (mathematics)</subject><ispartof>arXiv.org, 2024-05</ispartof><rights>2024. 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title	Carleson measures for weighted Bergman--Zygmund spaces
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