Journal of Shanghai University(Natural Science Edition) ›› 2014, Vol. 20 ›› Issue (6): 726-732.doi: 10.3969/j.issn.1007-2861.2014.02.006

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Half-Discrete Hilbert-Type Inequality Containing Logarithmic Kernel

YANG Bi-cheng1, CHEN Qiang2   

  1. 1. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China;
    2. Department of Computer Science, Guangdong University of Education, Guangzhou 510303, China
  • Received:2013-09-30 Online:2014-12-23 Published:2014-12-23

Abstract: Using a method of weight coefficients, complex analysis and parameterization,a half-discrete Hilbert-type inequality containing a logarithmic kernel and an optimal constant factor is given. Optimal extension with multi-parameters, equivalent forms and homogeneous forms for a particular parameter are deduced.

Key words: equivalent form, Hilbert-type inequality, parameter, weight coefficient

CLC Number: