Integral Criteria for Weighted Bloch Functions

The present manuscript gives analytic characterizations and interesting technique that involves the study of general ϖ -Besov classes of analytic functions by the help of analytic ϖ -Bloch functions. Certain special functions significant in both ϖ -Besov-norms and ϖ -Bloch norms framework and to introduce new important families of analytic classes. Interesting motivation of this concerned paper is to construct some new analytic function classes of general ϖ -Besov-type spaces via integrals on concerned functions view points. The introduced analytic ϖ -Bloch and ϖ -Besov type of functions with some interesting properties for these classes of function spaces are established within the constructions of their norms. Using the defined analytic function spaces, various important relations are also derived.

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Integral Superposition-Type Operators on Some Analytic Function Spaces

Journal of Function Spaces ◽

10.1155/2021/5531955 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

A. El-Sayed Ahmed ◽

S. Omran

Keyword(s):

Analytic Function ◽

Entire Functions ◽

Bloch Space ◽

Function Spaces ◽

Superposition Operator ◽

Superposition Operators ◽

Type Spaces ◽

Analytic Function Spaces

All entire functions which transform a class of holomorphic Zygmund-type spaces into weighted analytic Bloch space using the so-called n -generalized superposition operator are characterized in this paper. Moreover, certain specific properties such as boundedness and compactness of the newly defined class of generalized integral superposition operators are discussed and established by using the concerned entire functions.

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Operator Norms and Essential Norms of Weighted Composition Operators from Analytic Function Spaces into Zygmund-type Spaces

Complex Analysis and Operator Theory ◽

10.1007/s11785-020-01018-x ◽

2020 ◽

Vol 14 (6) ◽

Author(s):

Shams Alyusof ◽

Flavia Colonna

Keyword(s):

Analytic Function ◽

Composition Operators ◽

Function Spaces ◽

Weighted Composition Operators ◽

Type Spaces ◽

Weighted Composition ◽

Operator Norms ◽

Analytic Function Spaces

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On traces of analytic Gp type spaces, mixed norm spaces and harmonic Bergman classes on certain polydomains

Filomat ◽

10.2298/fil1101001s ◽

2011 ◽

Vol 25 (1) ◽

pp. 1-19

Author(s):

Romi Shamoyan ◽

Olivera Mihic

Keyword(s):

Analytic Function ◽

Unit Ball ◽

Function Spaces ◽

Mixed Norm ◽

Mixed Norm Spaces ◽

Type Spaces ◽

Analytic Function Spaces

In this paper, we introduce new Qp type spaces and mixed norm analytic function spaces on polyballs and describe completely their traces on unit ball. Complete descriptions of traces of harmonic Bergman classes on products of unit balls of Rn and products of Rn+1 half spaces will be also provided.

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Estimates on Some General Classes of Holomorphic Function Spaces

Symmetry ◽

10.3390/sym13040528 ◽

2021 ◽

Vol 13 (4) ◽

pp. 528

Author(s):

Amnah Shammaky ◽

Ahmed El-Sayed Ahmed

Keyword(s):

Analytic Function ◽

Holomorphic Function ◽

Operator Theory ◽

Unit Disc ◽

Special Functions ◽

Function Spaces ◽

Type Operator ◽

Analytic Function Spaces

In this current manuscript, some general classes of weighted analytic function spaces in a unit disc are defined and studied. Special functions significant in both analytic T(p,q,m,s;Ψ) norms and analytic Ψ-Bloch norms serve as a framework for introducing new families of analytic classes. An application in operator theory is provided by establishing important properties of the composition-type operator Cϕ such as the boundedness and compactness with the help of the defined new classes.

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