Abstract
In this chapter, we demonstrate how some ideas originating in the analysis on groups can be applied in related settings without the group structure. In particular, in Chapter 7 we showed a number of Hardy and Rellich inequalities with weights expressed in terms of the so-called \(\mathcal{L}\)-gauge. There, the \(\mathcal{L}\)-gauge is a homogeneous quasi-norm on a stratified group which is obtained from the fundamental solution to the sub-Laplacian. At the same time, in Chapter 11 we used the fundamental solutions of the sub-Laplacian for the advancement of the potential theory on stratified groups, and in Section 7.3 fundamental solutions for the p-sub-Laplacian and their properties were used on polarizable Carnot groups for the derivation of further Hardy estimates in that setting.
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Ruzhansky, M., Suragan, D. (2019). Chapter 12 Hardy and Rellich Inequalities for Sums of Squares of Vector Fields. In: Hardy Inequalities on Homogeneous Groups. Progress in Mathematics, vol 327. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02895-4_13
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DOI: https://doi.org/10.1007/978-3-030-02895-4_13
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-02894-7
Online ISBN: 978-3-030-02895-4
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