Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 1073-1083

SHARP CAFFARELLI–KOHN–NIRENBERG INEQUALITIES ON STRATIFIED LIE GROUPS

Van Hoang Nguyen

Duy Tan University, Institute of Research and Development
Da Nang, Vietnam; vanhoang0610 'at' yahoo.com

Abstract. In this paper, we prove a family of sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups. Our result sharpens the inequalities obtained recently by Ruzhansky, Suragan and Yessirkegenov [22], and extend the classical Caffarelli–Kohn–Nirenberg inequalities to a new class of exponents (negative or smaller than 1) which we believe to be new in literature. Finally, we generalize our result to the more general setting of homogeneous groups with any homogeneous quasi-norm.

2010 Mathematics Subject Classification: Primary 26D10, 43A85, 22E30, 43A80.

Key words: Caffarelli–Kohn–Nirenberg inequalities, stratified Lie groups, sharp constants, optimal functions.

Reference to this article: V. H. Nguyen: Sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups. Ann. Acad. Sci. Fenn. Math. 43 (2018), 1073-1083.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4363