Littlewood-Paley formulas and Carleson measures for weighted Fock spaces induced by A^\infty-type weights.

We obtain Littlewood-Paley formulas for Fock spaces $\mathcal{F}^q_{\beta,\omega}$ induced by weights $\omega\in\Ainfty= \cup_{1\le p<\infty}A^{restricted}_{p}$, where $A^{restricted}_{p}$ is the class of weights such that the Bergman projection $P_\alpha$, on the classical Fock space $\mathcal{F...

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Detalhes bibliográficos
Autores: Cascante, Ma. Carme (Maria Carme), Fàbrega Casamitjana, Joan, Peláez Márquez, José Ángel
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/193240
Acesso em linha:https://hdl.handle.net/2445/193240
Access Level:acceso abierto
Palavra-chave:Funcions de variables complexes
Espais analítics
Anàlisi harmònica
Anàlisi funcional
Functions of complex variables
Analytic spaces
Harmonic analysis
Functional analysis
Descrição
Resumo:We obtain Littlewood-Paley formulas for Fock spaces $\mathcal{F}^q_{\beta,\omega}$ induced by weights $\omega\in\Ainfty= \cup_{1\le p<\infty}A^{restricted}_{p}$, where $A^{restricted}_{p}$ is the class of weights such that the Bergman projection $P_\alpha$, on the classical Fock space $\mathcal{F}^2_{\alpha}$, is bounded on $$\mathcal{L}^p_{\alpha,\om}:=\left\{f:\, \int_{\C}|f(z)|^pe^{-p\frac{\a}{2}|z|^2}\,\om(z)dA(z)<\infty \right\}. $$ Using these equivalent norms for $\mathcal{F}^q_{\beta,\omega}$ we characterize the Carleson measures for weighted Fock-Sobolev spaces $\mathcal{F}^{q,n}_{\beta,\om}$.