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Journal of Applied Mathematics and Computation

DOI:http://dx.doi.org/10.26855/jamc.2022.09.005

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Riemann-Stieltjes Operators Between Zygmund-Type Spaces

Zhitao Guo

School of Science, Henan Institute of Technology, Xinxiang, Henan, China.

*Corresponding author: Zhitao Guo

Date: September 8,2022 Hits: 264

Abstract

Let  be the open unit disk in the complex plane   . The integral operators and  , called the Riemann-Stieltjes operators or the Volterra type operators are defined by 

  and  ,

where   and   are analytic functions on and . Suppose   and  are Banach spaces and  is a linear operator. If there exists a positive constant  such that  for every , then we say that  is a bounded linear operator from   into  . If maps every bounded set of  to a relatively compact set of , then   is called a compact operator. The boundedness and compactness of a linear operator acting between the spaces of analytic functions are basic questions in operator theory, which has been extensively studied by many researchers. In this paper, we mainly investigate the boundedness and compactness of the above two Riemann-Stieltjes operators between Zygmund-type space.

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Riemann-Stieltjes Operators Between Zygmund-Type Spaces

How to cite this paper:  Zhitao Guo. (2022) Riemann-Stieltjes Operators Between Zygmund-Type Spaces. Journal of Applied Mathematics and Computation6(3), 332-342.

DOI: http://dx.doi.org/10.26855/jamc.2022.09.005