Trudinger–Moser inequalities on harmonic AN groups under Lorentz norms. (November 2019)

• Record Type: Journal Article
• Authors: Su, Dan; Yang, Qiaohua
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 439
• Page End: 454
• Publication Date: 2019-11
• Subjects: primary 35J20 46E35; Trudinger–Moser inequality -- Lorentz space -- Harmonic AN groups -- Sharp constant; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.06.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The main purpose of this paper is to establish sharp Trudinger–Moser type inequalities on harmonic A N groups S for functions whose gradient is in the Lorentz space L ( n, q ) . Our results show that even if S is not with strictly negative sectional curvature, one can also replace the norm ∫ S | ∇ S u | n d V + ∫ S | u | n d V by ∫ S | ∇ S u | n d V in the Trudinger–Moser type inequalities.