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Chapter 8 Geometric Hardy Inequalities on Stratified Groups

  • Michael Ruzhansky
  • Durvudkhan Suragan
Open Access
Chapter
Part of the Progress in Mathematics book series (PM, volume 327)

Abstract

Given a domain in the space, the ‘geometric’ version of Hardy inequalities usually refers to the Hardy type inequalities where the weight is given in terms of the distance to the boundary of the domain. In this chapter we discuss L2 and Lp versions of the geometric Hardy inequality on the stratified group \(\mathbb{G}\). For the clarity of the exposition, we first deal with the half-space domains, and then with more general convex domains.

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Authors and Affiliations

  • Michael Ruzhansky
    • 1
    • 2
    • 3
  • Durvudkhan Suragan
    • 4
  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Department of Mathematics: Analysis, Logic and Discrete MathematicsGhent UniversityGhentBelgium
  3. 3.School of Mathematical SciencesQueen Mary University of LondonLondonUK
  4. 4.Department of MathematicsNazarbayev UniversityAstanaKazakhstan

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