Abstract
They are the famous Hilbert integral inequalities, where the constant factors π2 and π are the best possible. And the equalities in (1.1) and (1.2) hold if and only if f (x) = 0, or g(x) = 0. These results can be found in papers [1] and [2]. Owing to the importance of the Hilbert inequality and the Hilbert type inequality in Mathematical analysis and applications, some mathematicians have been studying them. Recently, various refinements, extensions and generalizations of (1.2) appear in a great deal of the articles (such as [3]–[10] etc.). However, the research articles of (1.1) are few. The aim of the present paper is to build an inequality of the form
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