Chapter 10 Function Spaces on Homogeneous Groups

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


In this chapter, we describe several function spaces on homogeneous groups. The origins of the extensive use of homogeneous groups in analysis go back to the book [FS82] of Folland and Stein where Hardy spaces on homogeneous groups have been thoroughly analysed. It turns out that several other function spaces can be defined on homogeneous groups since their main structural properties essentially depend only on the group and dilation structures. Thus, in this chapter we carry out such a construction for Morrey and Campanato spaces and analyse their main properties. Moreover, we describe a version of Sobolev spaces associated to the Euler operator. We call such spaces the Euler–Hilbert–Sobolev spaces.

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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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