Obtaining upper bounds of heat kernels from lower bounds
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AbstractWe show that a near-diagonal lower bound of the heat kernel of a Dirichlet form on a metric measure space with a regular measure implies an on-diagonal upper bound. If in addition the Dirichlet form is local and regular, then we obtain a full off-diagonal upper bound of the heat kernel provided the Dirichlet heat kernel on any ball satisfies a near-diagonal lower estimate. This reveals a new phenomenon in the relationship between the lower and upper bounds of the heat kernel. (C) 2007 Wiley Periodicals, Inc.
All Author(s) ListGriogor'yan A, Hu JX, Lau KS
Journal nameCommunications on Pure and Applied Mathematics
Year2008
Month5
Day1
Volume Number61
Issue Number5
PublisherJOHN WILEY & SONS INC
Pages639 - 660
ISSN0010-3640
eISSN1097-0312
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesMathematics; MATHEMATICS; Mathematics, Applied; MATHEMATICS, APPLIED

Last updated on 2021-11-01 at 23:53