An integral representation for besov and lipschitz spaces

Kehe Zhu

doi:10.1017/S1446788714000469

An integral representation for besov and lipschitz spaces

Kehe Zhu

Mathematics and Statistics

University at Albany

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

It is well known that functions in the analytic Besov space B₁ on the unit disk D admit an integral representation f(z) =f_D-w/1-zwdμ(w), where μ is a complex Borel measure with |μ|(D). We generalize this result to all Besov spaces B_p with 0<p≤ 1 and all Lipschitz spaces Λ_t with t>1. We also obtain a version for Bergman and Fock spaces.

Original language	English
Pages (from-to)	129-144
Number of pages	16
Journal	Journal of the Australian Mathematical Society
Volume	98
Issue number	1
DOIs	https://doi.org/10.1017/S1446788714000469
State	Published - Feb 3 2015

Keywords

Berezin transform
Bergman spaces
Besov spaces
Carleson measures
Fock spaces
Lipschitz spaces
atomic decomposition

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abstract = "It is well known that functions in the analytic Besov space B1 on the unit disk D admit an integral representation f(z) =fD-w/1-zwdμ(w), where μ is a complex Borel measure with |μ|(D). We generalize this result to all Besov spaces Bp with 0t with t>1. We also obtain a version for Bergman and Fock spaces.",

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AB - It is well known that functions in the analytic Besov space B1 on the unit disk D admit an integral representation f(z) =fD-w/1-zwdμ(w), where μ is a complex Borel measure with |μ|(D). We generalize this result to all Besov spaces Bp with 0t with t>1. We also obtain a version for Bergman and Fock spaces.

KW - Berezin transform

KW - Bergman spaces

KW - Besov spaces

KW - Carleson measures

KW - Fock spaces

KW - Lipschitz spaces

KW - atomic decomposition

UR - https://www.scopus.com/pages/publications/84920158470

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JF - Journal of the Australian Mathematical Society

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ER -

An integral representation for besov and lipschitz spaces

Abstract

Keywords

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