Parameter Conditions for Boundedness of Two Integral Operators in Weighted Lebsgue Space and Calculation of Operator Norms-Reference-Cited by-同舟云学术

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Parameter Conditions for Boundedness of Two Integral Operators in Weighted Lebsgue Space and Calculation of Operator Norms

Published:2024-01-18 Issue:1 Volume:13 Page:58
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Zhang Lijuan¹,He Bing²^ORCID,Hong Yong¹

Affiliation:

1. Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China

2. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China

Abstract

Firstly, Hilbert-type integral inequalities with best constant factors are established for two non-homogeneous kernels. Then, by utilizing the relationship between the Hilbert-type inequality and the integral operator of same kernel, the parameter conditions for two integral operators with non-homogeneous kernels in weighted Lebesgue space to be bounded and the formula for calculating the operator norm are obtained.

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/1/58/pdf

Reference26 articles.

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2. On Hilbert’s integral inequality;Yang;J. Math. Anal. Appl.,1998

3. General Hilbert’s and Hardy’s inequalities;Math. Inequal. Appl.,2005

4. Note on new extensions of Hilbert’s integral inequality;Kuang;J. Math. Anal. Appl.,1999

5. Some new type Hilbert integral inequalities;Zhao;J. Math. Anal. Appl.,2001

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