Optimal matching parameters of the inverse Hilbert-type integral inequality with quasihomogeneous kernels and their applications

Yong Hong; Mingjun Feng; Bing He

doi:10.3842/umzh.v74i4.7366

Yong Hong Department of Applied Mathematics, Guangzhou Huashang College, China
Mingjun Feng Department of Mathematics, Guangdong University of Education, Guangzhou, China
Bing He Department of Mathematics, Guangdong University of Education, Guangzhou, China

DOI: https://doi.org/10.3842/umzh.v74i4.7366

Keywords: Inverse Hilbert type integral inequality; Quasi-homogeneous kernel; Optimal matching parameter; Integral operator

Abstract

UDC 517.9

By using the inverse Hölder inequality and the weight function method, we establish the inverse Hilbert-type integral inequality. In the case of a quasihomogeneous kernel, we obtain the necessary and sufficient conditions for the optimal matching parameters. Finally, their applications in the operator theory are discussed.

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