The Euclidean Onofri inequality in higher dimensions

Manuel Del Pino, Jean Dolbeault

Research output: Contribution to journalArticlepeer-review

8 Citations (SciVal)


The classical Onofri inequality in the two-dimensional sphere assumes a natural form in the plane when transformed via stereographic projection. We establish an optimal version of a generalization of this inequality in the d-dimensional Euclidean space for any d≥2, by considering the endpoint of a family of optimal Gagliardo-Nirenberg interpolation inequalities. Unlike the two-dimensional case, this extension involves a rather unexpected Sobolev-Orlicz norm, as well as a probability measure no longer related to stereographic projection.

Original languageEnglish
Pages (from-to)3600-3611
Number of pages12
JournalInternational Mathematics Research Notices
Issue number15
Publication statusPublished - 12 Aug 2013

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'The Euclidean Onofri inequality in higher dimensions'. Together they form a unique fingerprint.

Cite this