On the equivalence between an Onofri-type inequality by Del Pino–Dolbeault and the sharp logarithmic Moser–Trudinger inequality
Year: 2025
Type: article
Abstract: In this paper we consider the N-dimensional Euclidean Onofri inequality proved by del Pino and Dolbeault (Int Math Res Not IMRN 15:3600–3611, 2013) for smooth compactly supported functions in $$\mathbb {R}^N$$ R N , $$N \ge 2$$ N ≥ 2 . We extend the inequality to a suitable weighted Sobolev space, although no clear connection with standard Sobolev spaces on $$\mathbb {S}^N$$ S N through stereographic projection is present, except for the planar case. Moreover, in any dimension $$N \ge 2$$ N ≥ 2 , we show that the Euclidean Onofri inequality is equivalent to the logarithmic Moser–Trudinger inequality with sharp constant proved by Carleson and Chang (Bull Sci Math 110(2):113–127, 1986) for balls in $$\mathbb {R}^N$$ R N .
Institution: University of Bari Aldo Moro
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4407167897