Toeplitz operators with symbols in L1(D) on Bergman spaces with variable exponent

Gerardo A. Chacón; Gerardo R. Chacón; Humberto Rafeiro

doi:10.1007/s43034-025-00469-7

Toeplitz operators with symbols in L1(D) on Bergman spaces with variable exponent

Gerardo A. Chacón
, Gerardo R. Chacón
, Humberto Rafeiro

Department of Mathematical Sciences

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

Abstract

We establish a boundary condition on the variable exponent p, for which the operators Uz:f↦(f∘φz)φz′ are bounded in Ap(·)(D). This boundary condition enables us to investigate the boundedness and compactness of Toeplitz operators Tφ with symbols φ in L1(D), via the functions z↦‖UzTφUz(1)‖Lp(·)(D) and z↦‖UzTφ¯Uz(1)‖Lp(·)(D).

Original language	English
Article number	79
Journal	Annals of Functional Analysis
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/s43034-025-00469-7
Publication status	Published - Oct 2025

Keywords

Bergman spaces
Toeplitz operators
Variable exponent spaces

ASJC Scopus subject areas

Analysis

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10.1007/s43034-025-00469-7

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title = "Toeplitz operators with symbols in L1(D) on Bergman spaces with variable exponent",

abstract = "We establish a boundary condition on the variable exponent p, for which the operators Uz:f↦(f∘φz)φz′ are bounded in Ap(·)(D). This boundary condition enables us to investigate the boundedness and compactness of Toeplitz operators Tφ with symbols φ in L1(D), via the functions z↦‖UzTφUz(1)‖Lp(·)(D) and z↦‖UzTφ¯Uz(1)‖Lp(·)(D).",

keywords = "Bergman spaces, Toeplitz operators, Variable exponent spaces",

author = "Chac{\'o}n, \{Gerardo A.\} and Chac{\'o}n, \{Gerardo R.\} and Humberto Rafeiro",

note = "Publisher Copyright: {\textcopyright} Tusi Mathematical Research Group (TMRG) 2025.",

year = "2025",

month = oct,

doi = "10.1007/s43034-025-00469-7",

language = "English",

volume = "16",

journal = "Annals of Functional Analysis",

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TY - JOUR

T1 - Toeplitz operators with symbols in L1(D) on Bergman spaces with variable exponent

AU - Chacón, Gerardo A.

AU - Chacón, Gerardo R.

AU - Rafeiro, Humberto

N1 - Publisher Copyright: © Tusi Mathematical Research Group (TMRG) 2025.

PY - 2025/10

Y1 - 2025/10

N2 - We establish a boundary condition on the variable exponent p, for which the operators Uz:f↦(f∘φz)φz′ are bounded in Ap(·)(D). This boundary condition enables us to investigate the boundedness and compactness of Toeplitz operators Tφ with symbols φ in L1(D), via the functions z↦‖UzTφUz(1)‖Lp(·)(D) and z↦‖UzTφ¯Uz(1)‖Lp(·)(D).

AB - We establish a boundary condition on the variable exponent p, for which the operators Uz:f↦(f∘φz)φz′ are bounded in Ap(·)(D). This boundary condition enables us to investigate the boundedness and compactness of Toeplitz operators Tφ with symbols φ in L1(D), via the functions z↦‖UzTφUz(1)‖Lp(·)(D) and z↦‖UzTφ¯Uz(1)‖Lp(·)(D).

KW - Bergman spaces

KW - Toeplitz operators

KW - Variable exponent spaces

UR - https://www.scopus.com/pages/publications/105018181732

UR - https://www.scopus.com/pages/publications/105018181732#tab=citedBy

U2 - 10.1007/s43034-025-00469-7

DO - 10.1007/s43034-025-00469-7

M3 - Article

AN - SCOPUS:105018181732

SN - 2639-7390

VL - 16

JO - Annals of Functional Analysis

JF - Annals of Functional Analysis

IS - 4

M1 - 79

ER -

Toeplitz operators with symbols in L1(D) on Bergman spaces with variable exponent

Abstract

Keywords

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