A generalization of Toeplitz operators on the Bergman space

2013/11/28 by Daniel Suárez, Suárez, Daniel
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.FA

paper · pdf · doi:10.48550/arxiv.1311.7420

17 pages

arxiv created 2013/11/28 · openalex publication_date 2013/11/28 · arxiv updated 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If μ is a finite measure on the unit disc and k≥ 0 is an integer, we study a generalization derived from Englis's work, T_μ^(k), of the traditional Toeplitz operators on the Bergman space A², which are the case k=0. Among other things, we prove that when μ≥ 0, these operators are bounded if and only if μ is a Carleson measure, and we obtain some estimates for their norms.

Related

• Toeplitz operators and Carleson measure between weighted Bergman spaces induced by regular weights
• Carleson measures and Toeplitz operators on small Bergman spaces on the ball
• Carleson Measures and Toeplitz operators for weighted Bergman spaces on the unit ball
• Toeplitz operators via Carleson measures On β-modified Bergman Spaces
• The essential norm of Toeplitz operators between Bergman spaces induced by doubling weights