Titlebook: Hardy Inequalities on Homogeneous Groups; 100 Years of Hardy I Michael Ruzhansky,Durvudkhan Suragan Book‘‘‘‘‘‘‘‘ 2019 The Editor(s) (if app

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0743-1643 er‘s sums of squares and their fundamental solutions. ..This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developm978-3-030-02895-4Series ISSN 0743-1643 Series E-ISSN 2296-505X

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https://doi.org/10.1007/978-3-030-02895-4Rellich inequality; stratified group; anisotropic analysis; potential theory; functional inequalities on

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Chapter 2 Hardy Inequalities on Homogeneous Groups,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.

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Chapter 5 Integral Hardy Inequalities on Homogeneous Groups,In this chapter we discuss the integral form of Hardy inequalities where instead of estimating a function by its gradient, we estimate the integral by the function itself.

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Chapter 6 Horizontal Inequalities on Stratified Groups,In this chapter we discuss versions of some of the inequalities from the previous chapters in the setting of stratified groups. Because of the stratified structure here we can use the horizontal gradient in the estimates.

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Chapter 11 Elements of Potential Theory on Stratified Groups,In this chapter, we discuss elements of the potential theory and the theory of boundary layer operators in the setting of stratified groups. The main tools for this analysis are the fundamental solution for the sub-Laplacian and Green’s identities established in Section 1.4.4.