Hardy-Knopp Type Inequalities

Ravi P. Agarwal, Donal O’Regan and Samir H. Saker
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Ravi P. Agarwal: Texas A&M University–Kingsville, Department of Mathematics
Donal O’Regan: National University of Ireland, School of Mathematics Statistics and Applied Mathematics
Samir H. Saker: Mansoura University, Department of Mathematics

Chapter Chapter 7 in Hardy Type Inequalities on Time Scales, 2016, pp 221-294 from Springer

Abstract: Abstract This chapter considers Hardy-Knopp type inequalities on an arbitrary time scale 𝕋 $$ \mathbb{T} $$ . One-dimensional, two-dimensional and multidimensional versions Hardy-Knopp type inequalities are considered. Moreover, Hardy-Knopp type inequalities for several functions and refinement inequalities of Hardy-Knopp type with general kernels and Hardy-Knopp type on measure spaces are also discussed in this chapter. This chapter (with six sections) is organized as follows. In Sect. 7.1, we present a time scale version of inequalities of one dimension and then extend these inequalities to inequalities with two variables. In Sect. 7.2, we present some results for inequalities with two functions and in Sect. 7.3 we state and prove a number of Hardy-Knopp type inequalities on time scales using a convexity technique. In Sect. 7.4, we present some refinements of Hardy type inequalities with kernels. In Sect. 7.5, we generalize some delta-integral inequalities of Hardy type on time scales to diamond-α integrals.

Keywords: Hardy-type Inequalities; Time Scale Version; General Kernel; Convexity Technique; Delta Function Integration (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-44299-0_7

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DOI: 10.1007/978-3-319-44299-0_7

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