Toeplitz Operators on Variable Exponent Bergman Spaces

Chacón, Gerardo; Rafeiro, Humberto

doi:10.1007/s00009-016-0701-0

Cited by 13 publications

(8 citation statements)

References 23 publications

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“…One natural question is to ask whether this operator can be extended boundedly to the space A p Á ðÞ  ðÞ . This question is addressed in [31] were a characterization of the boundedness and compactness of T φ is found in terms of Carleson measures and the Berezin transform associated with T φ . This type of results are sometimes referred to as Axler-Zheng theorems, and similar questions looking to establish the relation between the Berezin transform of a finite product of Toeplitz operators with its compactness have been addressed by several authors; a survey of this type of results is given in [32].…”

Section: Operators In Variable Exponent Bergman Spacesmentioning

confidence: 99%

Variable Exponent Spaces of Analytic Functions

Chacón¹

2020

Advances in Complex Analysis and Applications

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Variable exponent spaces are a generalization of Lebesgue spaces in which the exponent is a measurable function. Most of the research done in this topic has been situated under the context of real functions. In this work, we present two examples of variable exponent spaces of analytic functions: variable exponent Hardy spaces and variable exponent Bergman spaces. We will introduce the spaces together with some basic properties and the main techniques used in the context. We will show that in both cases, the boundedness of the evaluation functionals plays a key role in the theory. We also present a section of possible directions of research in this topic.

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Section: Operators In Variable Exponent Bergman Spacesmentioning

confidence: 99%

Variable Exponent Spaces of Analytic Functions

Chacón¹

2020

Advances in Complex Analysis and Applications

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“…In this section, we show an example of a variable log −Hölder continuous exponent p(·) for which H p(·) (D) differs from all classical spaces H p (D). Define p : [0, 2π] → [2,3] as…”

Section: An Examplementioning

confidence: 99%

“…For example, in [9] a version of BM O spaces with variable exponents is considered. Bergman spaces with variable exponents have been studied in [1,2,3] and a different approach has been taken in [10] and [11], much of the research done in the area assume the log-Hölder condition on the exponent, which is a growth condition that usually guarantees the boundedness of a Hardy-Littlewood maximal operator in a related space. One case of function spaces on unbounded domains have been studied in [18].…”

Section: Introductionmentioning

confidence: 99%

Analytic variable exponent Hardy spaces

Chacón¹

2019

Adv. Oper. Theory

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“…Recently, in [2], Chacón and Rafeiro introduced variable exponent Bergman spaces on the open unit disk, they proved that polynomials are dense in these spaces and the Bergman projection and the Berezin transform are bounded. Then in [3] and [4], the authors characterized Toeplitz operators and Carleson measures for variable exponent Bergman spaces, which are generalizations of constant exponent Bergman spaces. In [11], some derivative and Lipschitz type characterizations of variable exponent Bergman spaces in several variables were obtained by Ma and Xu.…”

Section: Introductionmentioning

confidence: 99%