Work

Relaxing the positivity assumption on the symbol of a Bergman-Toeplitz operator

Year: 2025

Type: article

Abstract: We examine Toeplitz operators on weighted Bergman spaces A V p A_\mathcal {V}^p , 1 > p > ∞ 1 > p > \infty , on the unit disk of C \mathbb {C} with symbols satisfying the simple geometric condition that the values are contained in an angle with vertex in the origin and magnitude less than π \pi . The condition is used to relax the conventional positivity assumption of the symbol, yet it is possible to give characterizations of the boundedness and compactness of such Toeplitz operators. The radial weight V \mathcal {V} defining the space A V p A_\mathcal {V}^p may be doubling or exponentially decreasing, but the geometric condition depends only on the symbol and not on V \mathcal {V} . It is known that there are significant differences between doubling and exponential weights for example as regards to the boundedness of Bergman projections. Nevertheless, we give a unified approach which includes both weight classes.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17430

Authors: Sinem Sönmez, Jari Taskinen

Institutions: University of Helsinki, Altınbaş University

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Türkiye Bilimsel ve Teknolojik Araştırma Kurumu

Award: G1377996984