Abstract
AbstractIn this chapter, using the methods of weight functions and technique of real analysis, a half-discrete Hilbert-type inequality with a homogeneous kernel and a best possible constant factor is provided. Some equivalent representations, two types of reverses, the operator expressions as well as some particular examples are obtained. Furthermore, we also consider some strengthened versions of half-discrete Hilbert’s inequality relating to Euler constant, the related inequalities and operators with the non-homogeneous kernel, and two kinds of compositions of two operators in certain conditions.KeywordsHalf-discrete Hilbert-type inequalityWeight functionEquivalent formHilbert-type operatorComposition
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