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›› 2016, Vol. 33 ›› Issue (6): 729-735.DOI: 10.7523/j.issn.2095-6134.2016.06.002

• Research Articles • Previous Articles     Next Articles

On a two-parameter Hilbert-type integral operator and its applications

SUN Wenbing, LIU Qiong   

  1. Department of Science and Information Science, Shaoyang University, Shaoyang 422000, Hunan, China
  • Received:2016-03-18 Online:2016-11-15
  • Supported by:

    Supported by the National Natural Science Foundation of China(11171280)

Abstract:

In this work, by introducing two parameters λ1 and λ2 and using the method of weight function and the technique of functional analysis, a two-parameter Hilbert-type integral operator is defined and the norm of the operator is given. As applications, a few improved results and some new Hilbert-type integral inequalities with the particular kernels are obtained.

Key words: two-parameter Hilbert-type integral operator, norm, weight function, the best constant factor, Hilbert-type integral inequality

CLC Number: