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Volume 13
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10.3390/axioms13010058
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Article

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

by
Lijuan Zhang
1,
Bing He
2,* and
Yong Hong
1
1
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China
2
Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(1), 58; https://doi.org/10.3390/axioms13010058
Submission received: 15 December 2023 / Revised: 8 January 2024 / Accepted: 15 January 2024 / Published: 18 January 2024
Versions Notes

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.
Keywords: weighted Lebesgue space; integral operator; non-homogeneous kernel; bounded operator; operator norm; Hilbert-type inequality weighted Lebesgue space; integral operator; non-homogeneous kernel; bounded operator; operator norm; Hilbert-type inequality

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MDPI and ACS Style

Zhang, L.; He, B.; Hong, Y. Parameter Conditions for Boundedness of Two Integral Operators in Weighted Lebsgue Space and Calculation of Operator Norms. Axioms 2024, 13, 58. https://doi.org/10.3390/axioms13010058

AMA Style

Zhang L, He B, Hong Y. Parameter Conditions for Boundedness of Two Integral Operators in Weighted Lebsgue Space and Calculation of Operator Norms. Axioms. 2024; 13(1):58. https://doi.org/10.3390/axioms13010058

Chicago/Turabian Style

Zhang, Lijuan, Bing He, and Yong Hong. 2024. "Parameter Conditions for Boundedness of Two Integral Operators in Weighted Lebsgue Space and Calculation of Operator Norms" Axioms 13, no. 1: 58. https://doi.org/10.3390/axioms13010058

APA Style

Zhang, L., He, B., & Hong, Y. (2024). Parameter Conditions for Boundedness of Two Integral Operators in Weighted Lebsgue Space and Calculation of Operator Norms. Axioms, 13(1), 58. https://doi.org/10.3390/axioms13010058

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