Affiliation:
1. School of Mathematics and Statistics , Northwestern Polytechnical University , Xi’an , 710129 , P. R. China
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.
Funder
National Natural Science Foundation of China
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