Brownian Motion and Harmonic Analysis on Sierpinski Carpets
- 1 August 1999
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 51 (4) , 673-744
- https://doi.org/10.4153/cjm-1999-031-4
Abstract
We consider a class of fractal subsets ofdformed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to constants, the best possible; construct a locally isotropic diffusionXand determine its basic properties; and extend some classical Sobolev and Poincaré inequalities to this setting.Keywords
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