The Duren–Carleson Theorem in Tube Domains over Symmetric Cones

David Békollé; Benoit F. Sehba; Edgar L. Tchoundja

doi:10.1007/s00020-016-2336-8

The Duren–Carleson Theorem in Tube Domains over Symmetric Cones

David Békollé, Benoit F. Sehba, Edgar L. Tchoundja

Department of Mathematics

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

3 Citations (Scopus)

Abstract

In the setting of tube domains over symmetric cones, we determine a necessary and sufficient condition on a Borel measure μ so that the Hardy space Hp,1≤p<∞, continuously embeds in the weighted Lebesgue space L^q(T_Ω, dμ) with a larger exponent. Finally we use this result to characterize multipliers from H² ^m to Bergman spaces for every positive integer m.

Original language	English
Pages (from-to)	475-494
Number of pages	20
Journal	Integral Equations and Operator Theory
Volume	86
Issue number	4
DOIs	https://doi.org/10.1007/s00020-016-2336-8
Publication status	Published - 1 Dec 2016

Keywords

Bergman spaces
Hardy spaces
Symmetric cones

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10.1007/s00020-016-2336-8

Cite this

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abstract = "In the setting of tube domains over symmetric cones, we determine a necessary and sufficient condition on a Borel measure μ so that the Hardy space Hp,1≤p<∞, continuously embeds in the weighted Lebesgue space Lq(TΩ, dμ) with a larger exponent. Finally we use this result to characterize multipliers from H2 m to Bergman spaces for every positive integer m.",

keywords = "Bergman spaces, Hardy spaces, Symmetric cones",

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AU - Békollé, David

AU - Sehba, Benoit F.

AU - Tchoundja, Edgar L.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - In the setting of tube domains over symmetric cones, we determine a necessary and sufficient condition on a Borel measure μ so that the Hardy space Hp,1≤p<∞, continuously embeds in the weighted Lebesgue space Lq(TΩ, dμ) with a larger exponent. Finally we use this result to characterize multipliers from H2 m to Bergman spaces for every positive integer m.

AB - In the setting of tube domains over symmetric cones, we determine a necessary and sufficient condition on a Borel measure μ so that the Hardy space Hp,1≤p<∞, continuously embeds in the weighted Lebesgue space Lq(TΩ, dμ) with a larger exponent. Finally we use this result to characterize multipliers from H2 m to Bergman spaces for every positive integer m.

KW - Bergman spaces

KW - Hardy spaces

KW - Symmetric cones

UR - https://www.scopus.com/pages/publications/84996587651

U2 - 10.1007/s00020-016-2336-8

DO - 10.1007/s00020-016-2336-8

M3 - Article

AN - SCOPUS:84996587651

SN - 0378-620X

VL - 86

SP - 475

EP - 494

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -

The Duren–Carleson Theorem in Tube Domains over Symmetric Cones

Abstract

Keywords

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