Abstract

This chapter is devoted to Hardy inequalities and the analysis of their remainders in different forms. Moreover, we discuss several related inequalities such as Rellich inequalities and uncertainty principles.

Highlights

  • This chapter is devoted to Hardy inequalities and the analysis of their remainders in different forms

  • In the setting of Part 1 above the remainder formula (2.3) for the Euclidean norm | · |E in Rn was analysed by Ioku, Ishiwata and Ozawa [IIO17]. 2.1

  • G is a homogeneous group of homogeneous dimension Q ≥ 3

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Summary

Chapter 2 Hardy Inequalities on Homogeneous Groups

This chapter is devoted to Hardy inequalities and the analysis of their remainders in different forms. Some statements will hold for Q ≥ 2 or for Q ≥ 3 but we will be specifying this explicitly in formulations when needed

Hardy inequalities and sharp remainders
Hardy inequality and uncertainty principle
Weighted Hardy inequalities
Hardy inequalities with super weights
Hardy inequalities of higher order with super weights
Two-weight Hardy inequalities
Critical Hardy inequalities
Another type of critical Hardy inequality
Critical Hardy inequalities of logarithmic type
Remainder estimates
Remainder estimates for Lp-weighted Hardy inequalities
Critical and subcritical Hardy inequalities
A family of Hardy–Sobolev type inequalities on quasi-balls
Improved Hardy inequalities on quasi-balls
Stability of Hardy inequalities
Stability of Hardy inequalities for radial functions
Stability of Hardy inequalities for general functions
Stability of critical Hardy inequality
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