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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/160808 |
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| _version_ | 1850232584349417472 |
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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). |
| format | Article |
| id | doaj-art-0af3c6a2dfe64f7eb7e99bb9da04de6e |
| institution | OA Journals |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |