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Weighted higher order exponential type inequalities in metric spaces and applications
Georgian Mathematical Journal ( IF 0.8 ) Pub Date : 2020-04-15 , DOI: 10.1515/gmj-2020-2059
Huiju Wang 1 , Pengcheng Niu 1
Affiliation  

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.

中文翻译:

度量空间和应用中的加权高阶指数类型不等式

在本文中,我们建立了测地空间中的加权高阶指数型不等式 Xdμ通过提出抽象的高阶庞加莱不等式。在非加权情况下,这些也是新的。作为应用程序,我们在测地环境中获得了加权的Trudinger定理,并为分层Lie组上定义的Folland-Stein型Sobolev空间中的函数提供了加权的高阶指数类型估计。还给出了连通齐次空间中的高阶指数型不等式。
更新日期:2020-04-15
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