The Journal of the Indian Mathematical Society

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On a Half-Discrete Hilbert-Type Inequality with a Logarithmic Kernel


Affiliations
1 Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510 303, China
2 Department of Mathematics, University of Texas-Pan American 1201 W. University Drive, Edinburg, TX 78539, United States
     

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By using the way of weight functions and Hadamard's inequality, a half-discrete Hilbert-type inequality with a logarithmic kernel and a best constant factor is given. The extension with multi-parameters, the equivalent forms as well as the operator expressions are also considered.

Keywords

Hilbert-Type Inequality, Weight Function, Equivalent Form, Foundation Item.
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  • On a Half-Discrete Hilbert-Type Inequality with a Logarithmic Kernel

Abstract Views: 216  |  PDF Views: 0

Authors

Bicheng Yang
Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510 303, China
Lokenath Debnath
Department of Mathematics, University of Texas-Pan American 1201 W. University Drive, Edinburg, TX 78539, United States

Abstract


By using the way of weight functions and Hadamard's inequality, a half-discrete Hilbert-type inequality with a logarithmic kernel and a best constant factor is given. The extension with multi-parameters, the equivalent forms as well as the operator expressions are also considered.

Keywords


Hilbert-Type Inequality, Weight Function, Equivalent Form, Foundation Item.