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Potential Analysis

, Volume 50, Issue 2, pp 221–244 | Cite as

Littlewood-Paley Formulas and Carleson Measures for Weighted Fock Spaces Induced by \(A_{\infty }\)-Type Weights

  • Carme Cascante
  • Joan Fàbrega
  • José A. PeláezEmail author
Article
  • 41 Downloads

Abstract

We obtain Littlewood-Paley formulas for Fock spaces \({\mathcal {F}}_{\beta ,\omega }^{q}\) induced by weights \(\omega \in {A}_{\infty }^{restricted} = \cup _{1 \le p < \infty } {A}_{p}^{restricted}\), where \( {A}_{p}^{restricted} \) is the class of weights such that the Bergman projection Pα, on the classical Fock space \({\mathcal {F}}_{\alpha }^{2}\), is bounded on
$${\mathcal{L}}_{\alpha,\omega}^{p} := \left\{f:\, {\int}_{\mathbb{C}}|f(z)|^{p} e^{-p\frac{\alpha}{2}|z|^{2}}\,\omega(z)dA(z)<\infty \right\}. $$
Using these equivalent norms for \({\mathcal {F}}_{\beta ,\omega }^{q}\) we characterize the Carleson measures for weighted Fock-Sobolev spaces \({\mathcal {F}}_{\beta ,\omega }^{q,n}\).

Keywords

Fock spaces Littlewood-Paley formula Carleson measures Pointwise multipliers 

Mathematics Subject Classification (2010)

30H20 42B25 46E35 

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Notes

Acknowledgements

We would like to thank the referee his/her suggestions and observations which improved the exposition of the paper.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Carme Cascante
    • 1
  • Joan Fàbrega
    • 1
  • José A. Peláez
    • 2
    Email author
  1. 1.Departament de Matemàtiques i InformàticaUniversitat de BarcelonaBarcelonaSpain
  2. 2.Departamento de Análisis MatemáticoFacultad de CienciasMálagaSpain

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