Journal of Mahani Mathematical Research

Journal of Mahani Mathematical Research

Schatten class Toeplitz operators on Bergman spaces with almost standard weights

Document Type : Research Paper

Author
Kobra Esmaeili
Faculty of Engineering, Ardakan University, P. O. 184, Ardakan, Iran
10.22103/jmmr.2026.26719.1929
Abstract
We study Schatten class Toeplitz operators on weighted Bergman spaces induced by almost standard radial weights on the unit disk. We obtain a complete characterization of such operators generated by positive Borel measures. The characterization is given in terms of the Berezin transform, integrability of localized averages with respect to the M\"obius invariant measure, and discrete summability over pseudohyperbolic lattices. For Toeplitz operators generated by complex Borel measures, we establish sufficient conditions for Schatten class membership in terms of discrete lattice averages of the total variation, together with corresponding norm estimates. As an application, we derive Schatten class bounds for differences of such operators.
Keywords
Toeplitz operators
Schatten classes
weighted Bergman spaces
almost standard weights
complex measures
Subjects
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  • Receive Date 26 January 2026
  • Revise Date 04 May 2026
  • Accept Date 22 May 2026