Spaces of Lipschitz type on metric spaces and their applications

Dachun Yang Department of Mathematics, Beijing Normal University, Beijing 100875, People’s Republic of China Yong Lin Department of Mathematics, Information School, Renmin (People) University of China, Beijing 100872, People’s Republic of China

Functional Analysis mathscidoc:2207.12004

Proceedings of the Edinburgh Mathematical Society, 47, (3), 709-752, 2004.11
New spaces of Lipschitz type on metric-measure spaces are introduced and they are shown to be just the well-known Besov spaces or Triebel–Lizorkin spaces when the smooth index is less than 1. These theorems also hold in the setting of spaces of homogeneous type, which include Euclidean spaces, Riemannian manifolds and some self-similar fractals. Moreover, the relationships amongst these Lipschitz-type spaces, Hajłasz–Sobolev spaces, Korevaar–Schoen–Sobolev spaces, Newtonian Sobolev space and Cheeger–Sobolev spaces on metric-measure spaces are clarified, showing that they are the same space with equivalence of norms. Furthermore, a Sobolev embedding theorem, namely that the Lipschitz-type spaces with large orders of smoothness can be embedded in Lipschitz spaces, is proved. For metric-measure spaces with heat kernels, a Hardy–Littlewood–Sobolev theorem is establish, and hence it is proved that Lipschitz-type spaces with small orders of smoothness can be embedded in Lebesgue spaces.
No keywords uploaded!
[ Download ] [ 2022-07-07 11:12:12 uploaded by yonglin ] [ 88 downloads ] [ 0 comments ]
@inproceedings{dachun2004spaces,
  title={Spaces of Lipschitz type on metric spaces and their applications},
  author={Dachun Yang, and Yong Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707111212829123549},
  booktitle={Proceedings of the Edinburgh Mathematical Society},
  volume={47},
  number={3},
  pages={709-752},
  year={2004},
}
Dachun Yang, and Yong Lin. Spaces of Lipschitz type on metric spaces and their applications. 2004. Vol. 47. In Proceedings of the Edinburgh Mathematical Society. pp.709-752. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707111212829123549.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved