Weighted higher order exponential type inequalities in metric spaces and applications

Abstract

Abstract In this paper, we establish weighted higher order exponential type inequalities in the geodesic space ( X , d , μ ) {({X,d,\mu})} by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined on stratified Lie groups. A higher order exponential type inequality in a connected homogeneous space is also given.