Complex symmetric weighted composition operators on Bergman spaces and Lebesgue spaces

被引：4

作者：

Pham Viet Hai ^{[1
]}

Severiano, Osmar R. ^{[2
]}

机构：

[1] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, 1 Dai Co Viet, Hanoi, Vietnam

[2] Univ Fed Campina Grande, Univ Fed Paraiaba, Programa Assoc Pos Grad Matemat, Joao Pessoa, Paraiba, Brazil

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2022年 / 12卷 / 02期

关键词：

Weighted composition operator; Complex symmetry; Bergman space;

D O I：

10.1007/s13324-022-00651-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of conjugations. As it turns out, weighted composition operators enhanced by a symmetry must be bounded. Hermitian, and unitary weighted composition operators are proven to be complex symmetric with respect to an adapted and highly relevant conjugation. We classify which the linear fractional functions give rise to the complex symmetry of bounded composition operators. We end the paper with a natural link to complex symmetry in Lebesgue space.

引用

页数：33

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