Toeplitz operators and weighted composition operators on variable exponent Bergman spaces

2025/07/18 by Tong, Cezhong, Yang, Zicong, Zhou, Zehua · 1 citation
#30H20 #47B33 #47B35 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.13675

Abstract

In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson measures. Then they extended the results to the ball setting. In this paper, we further generalize those results to variable exponent Bergman spaces over the unit ball. Our proofs, when restricted to the case of constant variable, are new and simpler. Moreover, boundedness and compactness of Toeplitz operators on variable exponent Bergman spaces are also characterized.

Citations

• Carleson Measures and Toeplitz operators for weighted Bergman spaces on the unit ball
• Theory of Bergman Spaces in the Unit Ball of Cⁿ

Cited by

• Essential norm and Schatten class difference of weighted composition operators over the ball

Related

• Carleson Measures and Toeplitz operators for weighted Bergman spaces on the unit ball
• Difference of weighted composition operators on weighted Bergman spaces over the unit Ball
• Toeplitz operators and Carleson measure between weighted Bergman spaces induced by regular weights
• Compact differences of composition operators on Bergman spaces induced by doubling weights
• Difference of composition operators between weighted Bergman spaces on the unit ball