Weighted higher order exponential type inequalities in metric spaces and applications.

In this paper, we establish weighted higher order exponential type inequalities in the geodesic space (X, d, μ) 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. [ABSTRACT FROM AUTHOR]