Trudinger–Moser inequalities on harmonic AN groups under Lorentz norms. (November 2019) - Su, Dan; Yang, Qiaohua
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.