Equivalence conditions for on-diagonal upper bounds of heat kernels on self-similar spaces
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AbstractWe obtain the equivalence conditions for an on-diagonal upper bound of heat kernels on self-similar measure energy spaces. In particular, this upper bound of the heat kernel is equivalent to the discreteness of the spectrum of the generator of the Dirichlet form. and to the global Poincare inequality. The key ingredient of the proof is to obtain the Nash inequality from the global Poincare inequality. We give two examples of families of spaces where the global Poincare inequality is easily derived. They are the post-critically finite (p.c.f.) self-similar sets with harmonic structure and the products of self-similar measure energy spaces. (C) 2006 Elsevier Inc. All rights reserved.
All Author(s) ListGrigor'yan A, Hu JX, Lau KS
Journal nameJournal of Functional Analysis
Year2006
Month8
Day15
Volume Number237
Issue Number2
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Pages427 - 445
ISSN0022-1236
eISSN1096-0783
LanguagesEnglish-United Kingdom
KeywordsDirichlet form; heat kernel; on-diagonal upper bound; self-similar space
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2021-20-01 at 00:34