Multidimensional Hilbert-Type Integral Inequalities and Their Operators Expressions

Bicheng Yang ()
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Bicheng Yang: Guangdong University of Education

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 769-814 from Springer

Abstract: Abstract In this chapter, by the use of the methods of weight functions and techniques of Real Analysis, we provide a general multidimensional Hilbert-type integral inequality with a non-homogeneous kernel and a best possible constant factor. The equivalent forms, the reverses and some Hardy-type inequalities are obtained. Furthermore, we consider the operator expressions with the norm, some particular inequalities with the homogeneous kernel and a large number of particular examples.

Keywords: Multidimensional Hilbert-type integral inequality; Weight function; Equivalent form; Hilbert-type integral operator; Multidimensional Hilbert-type integral inequality; 26D15; 31A10; 47A07 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-06554-0_34

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DOI: 10.1007/978-3-319-06554-0_34

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