Acta mathematica scientia,Series A ›› 2024, Vol. 44 ›› Issue (4): 837-846.

Previous Articles     Next Articles

Parameter Conditions for Constructing Bounded Discrete Operators with Super-Homogeneous Kernel and Estimation of the Operator Norm

Hong Yong(),Zhao Qian*()   

  1. College of Data Science, Guangzhou Huashang College, Guangzhou 511300
  • Received:2023-07-17 Revised:2024-01-10 Online:2024-08-26 Published:2024-07-26
  • Supported by:
    Fundamental and Applied Basic Research Program of Guangdong Province(2022A1515012429);Guangzhou Huashang College Research Team Program(2021HSKT03)

Abstract:

Introducing the concept of super-homogeneous function, firstly constructing the Hilbert-type discrete inequality with super-homogeneous kernel, and then discussing discrete operator with super-homogeneous kernel by using the relationship between Hilbert-type inequality and operator with the same kernel, obtained the construction conditions for bounded discrete operators with super-homogeneous kernel in weighted normed sequence spaces, and a method for determining whether an operator is bounded or not and the estimation of operator norm are solved.

Key words: Super-homogeneous function, Bounded discrete operator, Weighted sequence spaces, Determination of bounded operators, Hilbert-type discrete inequality, Operator norm

CLC Number: 

  • O177
Trendmd