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Multidimensional Hilbert-Type Integral Inequalities and Their Operators Expressions

In: Topics in Mathematical Analysis and Applications

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  • Bicheng Yang

    (Guangdong University of Education)

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.

Suggested Citation

  • Bicheng Yang, 2014. "Multidimensional Hilbert-Type Integral Inequalities and Their Operators Expressions," Springer Optimization and Its Applications, in: Themistocles M. Rassias & László Tóth (ed.), Topics in Mathematical Analysis and Applications, edition 127, pages 769-814, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-06554-0_34
    DOI: 10.1007/978-3-319-06554-0_34
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    Cited by:

    1. Butt, Saad Ihsan & Yousaf, Saba & Akdemir, Ahmet Ocak & Dokuyucu, Mustafa Ali, 2021. "New Hadamard-type integral inequalities via a general form of fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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