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	Some notes on function spaces and Dirichlet forms on self-similar sets
	Liu, Yuan ; Wen, Zhi-Ying
	2010-05-06 ; 2010-05-06
关键词	sub-Gaussian heat kernel self-similar Dirichlet form effective resistance PARABOLIC HARNACK INEQUALITIES METRIC MEASURE-SPACES BROWNIAN-MOTION HARMONIC-ANALYSIS RESISTANCE FORMS FRACTALS Mathematics, Applied Mathematics
中文摘要	Grigor'yan, Hu and Lau [10] introduced sub-Gaussian heat kernels on general metric measure spaces and defined a family of function spaces to characterize the domain of associated Dirichlet forms. In this paper, we will improve their results about norm equivalence. As an application, we construct self-similar Dirichlet forms on a class of self-similar sets containing the Sierpinski gaskets and carpets. Then we prove the Poincare inequality and give effective resistance estimates by the self-similarity. Consequently, we have a new equivalent characterization of heat kernel estimates through function spaces with strong recurrent condition.
语种	英语 ; 英语
出版者	ADVANCED NONLINEAR STUDIES, INC ; SAN ANTONIO ; PO BOX 691204, SAN ANTONIO, TX 78269 USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/14106]
专题	清华大学
推荐引用方式 GB/T 7714	Liu, Yuan,Wen, Zhi-Ying. Some notes on function spaces and Dirichlet forms on self-similar sets[J],2010, 2010.
APA	Liu, Yuan,&Wen, Zhi-Ying.(2010).Some notes on function spaces and Dirichlet forms on self-similar sets..
MLA	Liu, Yuan,et al."Some notes on function spaces and Dirichlet forms on self-similar sets".(2010).

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