Derivatives of the Berezin Transform

For a rotation invariant domain Ω, we consider A2(Ω,μ) the Bergman space and we investigate some properties of the rank one projection A(z):=〈⋅,kz〉kz. We prove that the trace of all the strong derivatives of A(z) is zero. We also focus on the generalized Fock space A2(μm), where μm is the measure wi...

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Main Author: Hélène Bommier-Hato
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2012/160808
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author Hélène Bommier-Hato
author_facet Hélène Bommier-Hato
author_sort Hélène Bommier-Hato
collection DOAJ
description For a rotation invariant domain Ω, we consider A2(Ω,μ) the Bergman space and we investigate some properties of the rank one projection A(z):=〈⋅,kz〉kz. We prove that the trace of all the strong derivatives of A(z) is zero. We also focus on the generalized Fock space A2(μm), where μm is the measure with weight e-|z|m, m>0, with respect to the Lebesgue measure on ℂn and establish estimations of derivatives of the Berezin transform of a bounded operator T on A2(μm).
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language English
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series Journal of Function Spaces and Applications
spelling doaj-art-0af3c6a2dfe64f7eb7e99bb9da04de6e2025-08-20T02:03:08ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/160808160808Derivatives of the Berezin TransformHélène Bommier-Hato0LATP, UMR CNRS 6632, CMI, Université de Provence, 39 rue Fjoliot-Curie, 13453 Marseille Cedex 13, FranceFor a rotation invariant domain Ω, we consider A2(Ω,μ) the Bergman space and we investigate some properties of the rank one projection A(z):=〈⋅,kz〉kz. We prove that the trace of all the strong derivatives of A(z) is zero. We also focus on the generalized Fock space A2(μm), where μm is the measure with weight e-|z|m, m>0, with respect to the Lebesgue measure on ℂn and establish estimations of derivatives of the Berezin transform of a bounded operator T on A2(μm).http://dx.doi.org/10.1155/2012/160808
spellingShingle Hélène Bommier-Hato
Derivatives of the Berezin Transform
Journal of Function Spaces and Applications
title Derivatives of the Berezin Transform
title_full Derivatives of the Berezin Transform
title_fullStr Derivatives of the Berezin Transform
title_full_unstemmed Derivatives of the Berezin Transform
title_short Derivatives of the Berezin Transform
title_sort derivatives of the berezin transform
url http://dx.doi.org/10.1155/2012/160808
work_keys_str_mv AT helenebommierhato derivativesoftheberezintransform