Some estimates related to fractal measures and Laplacians on manifolds

Limin Sun Department of Mathematics, Hangzhou University

TBD mathscidoc:1701.332832

Arkiv for Matematik, 33, (1), 173-182, 1992.11
Let Δ be the Laplace-Beltrami operator on an$n$dimensional complete$C$^{∞}manifold$M$In this paper we establish an estimate of$e$^{$tΔ$}$(dμ)$valid for all$t$>0 where$dμ$is a locally uniformly α dimensional measure on$M$0≤α≤$n$The result is used to study the mapping properties of ($I$-$t$Δ)^{-β}considered as an operator from$L$^{$p$}$(M dμ)$to$L$^{$p$}$(M dx)$where$dx$is the Riemannian measure on$M β>(n−α)/2p′ 1/p+1/p′=1 1≤p≤∞$
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@inproceedings{limin1992some,
  title={Some estimates related to fractal measures and Laplacians on manifolds},
  author={Limin Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203545514251641},
  booktitle={Arkiv for Matematik},
  volume={33},
  number={1},
  pages={173-182},
  year={1992},
}
Limin Sun. Some estimates related to fractal measures and Laplacians on manifolds. 1992. Vol. 33. In Arkiv for Matematik. pp.173-182. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203545514251641.
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