On the boundedness of Toeplitz operators with radial symbols over weighted sup-norm spaces of holomorphic functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:493

Article

Bonet, Jose¹  Lusky, Wolfgang²  Taskinen, Jari³ 

[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada IUMPA, E-46071 Valencia, Spain

[2] Univ Paderborn, Inst Math, D-33098 Paderborn, Germany

[3] Univ Helsinki, Dept Math & Stat, POB 68, Helsinki 00014, Finland

关键词: Bergman space;    Toeplitz operator;    Bounded operator;    Weighted norm;    Sup-norm;   

DOI  :  10.1016/j.jmaa.2020.124515

来源: Elsevier

【 摘 要 】

We prove sufficient conditions for the boundedness and compactness of Toeplitz operators T-a in weighted sup-normed Banach spaces H-v(infinity) of holomorphic functions defined on the open unit disc D of the complex plane; both the weights v and symbols a are assumed to be radial functions on D. In an earlier work by the authors was shown that there exists a bounded, harmonic (thus non-radial) symbol a such that T-a is not bounded in any space H-v(infinity) with an admissible weight v. Here, we show that a mild additional assumption on the logarithmic decay rate of a radial symbol a at the boundary of D guarantees the boundedness of T-a. The sufficient conditions for the boundedness and compactness of T-a, in a number of variations, are derived from the general, abstract necessary and sufficient condition recently found by the authors. The results apply for a large class of weights satisfying the so called condition (B), which includes in addition to standard weight classes also many rapidly decreasing weights. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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