Chapter 4 Fractional Hardy Inequalities

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


In this chapter we present results concerning fractional forms of Hardy inequalities. Such a topic is well investigated in the Abelian Euclidean setting and we will be providing relevant references in the sequel. For a general survey of fractional Laplacians in the Euclidean setting see, e.g., [Gar17]. However, as usual, the general approach based on homogeneous groups allows one to get insights also in the Abelian case, for example, from the point of view of the possibility of choosing an arbitrary quasi-norm. Moreover, another application of the setting of homogeneous groups is that the results can be equally applied to both elliptic and subelliptic problems.

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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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