scholarly journals Integral Superposition-Type Operators on Some Analytic Function Spaces

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.

scholarly journals On composition operators inQKtype spaces

2007 ◽  
Vol 5 (2) ◽  
pp. 103-122 ◽  
Author(s):  
Marko Kotilainen
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Function Spaces ◽  
Analytic Mapping ◽  
Analytic Function Spaces

Letp≥1,q>-2and letK:[0,∞)→[0,∞)be nondecreasing. With a different choice ofp,q,K, the Banach spaceQK(p,q)coincides with many well-known analytic function spaces. Boundedness and compactness of the composition operatorCφfromα-Bloch spaceBαintoQK(p,q)are characterized by a condition depending only on analytic mappingφ:𝔻→𝔻. The same properties are also studied in the caseCφ:QK(p,q)→Bα.

scholarly journals Integral Criteria for Weighted Bloch Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
A. El-Sayed Ahmed ◽  
M. A. Bakhit
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Special Functions ◽  
Function Spaces ◽  
Bloch Functions ◽  
Function Classes ◽  
Type Spaces ◽  
Besov Norms ◽  
Analytic Function Spaces ◽  
Besov Type Spaces

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.

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

Filomat ◽  
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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