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

2025/07/26 by Hu, Xiaohe, Yang, Zicong
#30H20 #47B33 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.19745

Abstract

In this paper, we obtain the essential norm estimate for the difference of two weighted composition operators acting on standard weighted Bergman spaces over the unit ball. And we get some characterizations for the difference of weighted composition operators belonging to Schatten class, which has rarely been considered before. Our methods are fundamental, which involve Carleson measures and R-Berezin transform.

Citations

• Toeplitz operators and weighted composition operators on variable exponent Bergman spaces
• Compact differences of composition operators on Bergman spaces induced by doubling weights
• Theory of Bergman Spaces in the Unit Ball of Cⁿ

Related

• Difference of composition operators between weighted Bergman spaces on the unit ball
• Difference of weighted composition operators on weighted-type spaces in the unit ball
• Difference of weighted composition operators on weighted Bergman spaces over the unit Ball
• Essential norm and integration of a family of weighted composition operators
• Essential norm and a new characterization of weighted composition operators from weighted Bergman spaces and Hardy spaces into the Bloch space