scholarly journals Estimates on Some General Classes of Holomorphic Function Spaces

Symmetry ◽  
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.

scholarly journals Norm of a Volterra Integral Operator on Some Analytic Function Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hao Li ◽  
Songxiao Li
Keyword(s):  
Analytic Function ◽  
Integral Operator ◽  
Unit Disc ◽  
Function Spaces ◽  
Volterra Integral Operator ◽  
Analytic Function Spaces

Let f be an analytic function in the unit disc 𝔻. The Volterra integral operator If is defined as follows: If(h)(z)=∫0zf(w)h'(w)dw,h∈H(𝔻),z∈𝔻. In this paper, we compute the norm of If on some analytic function spaces.

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 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.

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