Sarason's Toeplitz product problem for a class of Fock spaces

Hélène Bommier-Hato; El Hassan Youssfi; Kehe Zhu

doi:10.1016/j.bulsci.2017.03.002

Sarason's Toeplitz product problem for a class of Fock spaces

Hélène Bommier-Hato
, El Hassan Youssfi
, Kehe Zhu

Mathematics and Statistics

University at Albany

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

21 Scopus citations

Abstract

Sarason's Toeplitz product problem asks when the operator T_uT_v‾ is bounded on various Hilbert spaces of analytic functions, where u and v are analytic. The problem is highly nontrivial for Toeplitz operators on the Hardy space and the Bergman space (even in the case of the unit disk). In this paper, we provide a complete solution to the problem for a class of Fock spaces on the complex plane. In particular, this generalizes an earlier result of Cho, Park, and Zhu.

Original language	English
Pages (from-to)	408-442
Number of pages	35
Journal	Bulletin des Sciences Mathematiques
Volume	141
Issue number	5
DOIs	https://doi.org/10.1016/j.bulsci.2017.03.002
State	Published - Jul 2017

Keywords

Berezin transform
Fock spaces
Sarason's conjecture
Sarason's problem
Toeplitz operator
Two-weight norm inequalities

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title = "Sarason's Toeplitz product problem for a class of Fock spaces",

abstract = "Sarason's Toeplitz product problem asks when the operator TuTv‾ is bounded on various Hilbert spaces of analytic functions, where u and v are analytic. The problem is highly nontrivial for Toeplitz operators on the Hardy space and the Bergman space (even in the case of the unit disk). In this paper, we provide a complete solution to the problem for a class of Fock spaces on the complex plane. In particular, this generalizes an earlier result of Cho, Park, and Zhu.",

keywords = "Berezin transform, Fock spaces, Sarason's conjecture, Sarason's problem, Toeplitz operator, Two-weight norm inequalities",

author = "H{\'e}l{\`e}ne Bommier-Hato and Youssfi, \{El Hassan\} and Kehe Zhu",

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T1 - Sarason's Toeplitz product problem for a class of Fock spaces

AU - Bommier-Hato, Hélène

AU - Youssfi, El Hassan

AU - Zhu, Kehe

PY - 2017/7

Y1 - 2017/7

N2 - Sarason's Toeplitz product problem asks when the operator TuTv‾ is bounded on various Hilbert spaces of analytic functions, where u and v are analytic. The problem is highly nontrivial for Toeplitz operators on the Hardy space and the Bergman space (even in the case of the unit disk). In this paper, we provide a complete solution to the problem for a class of Fock spaces on the complex plane. In particular, this generalizes an earlier result of Cho, Park, and Zhu.

AB - Sarason's Toeplitz product problem asks when the operator TuTv‾ is bounded on various Hilbert spaces of analytic functions, where u and v are analytic. The problem is highly nontrivial for Toeplitz operators on the Hardy space and the Bergman space (even in the case of the unit disk). In this paper, we provide a complete solution to the problem for a class of Fock spaces on the complex plane. In particular, this generalizes an earlier result of Cho, Park, and Zhu.

KW - Berezin transform

KW - Fock spaces

KW - Sarason's conjecture

KW - Sarason's problem

KW - Toeplitz operator

KW - Two-weight norm inequalities

UR - https://www.scopus.com/pages/publications/85020247089

U2 - 10.1016/j.bulsci.2017.03.002

DO - 10.1016/j.bulsci.2017.03.002

M3 - Article

SN - 0007-4497

VL - 141

SP - 408

EP - 442

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

IS - 5

ER -

Sarason's Toeplitz product problem for a class of Fock spaces

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Keywords

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