$L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups

Tohru Ozawa, Michael Ruzhansky, Durvudkhan Suragan

Research output: Contribution to journalArticle

Abstract

We prove $L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also discuss some of their consequences. Already in the abelian case of $\mathbb{R}^{n}$ our results provide new insights in view of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm.
LanguageEnglish
JournalQuarterly Journal of Mathematics
Publication statusAccepted/In press - 2018

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Sharp Constants
Homogeneous Groups
Nilpotent Lie Group
Euclidean
Norm

Keywords

  • math.FA
  • math.AP
  • 22E30, 43A80

Cite this

$L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups. / Ozawa, Tohru; Ruzhansky, Michael; Suragan, Durvudkhan.

In: Quarterly Journal of Mathematics, 2018.

Research output: Contribution to journalArticle

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