Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem

Thierry Coulhon; Adam Sikora

doi:10.1112/plms/pdm050

Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem

Thierry Coulhon^*, Adam Sikora

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

136 Citations (Scopus)

Abstract

We prove that in the presence of L² Gaussian estimates, the so-called Davies-Gaffney estimates, on-diagonal upper bounds imply precise off-diagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces.

Original language	English
Pages (from-to)	507-544
Number of pages	38
Journal	Proceedings of the London Mathematical Society
Volume	96
Issue number	2
DOIs	https://doi.org/10.1112/plms/pdm050
Publication status	Published - Mar 2008
Externally published	Yes

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title = "Gaussian heat kernel upper bounds via the Phragm{\'e}n-Lindel{\"o}f theorem",

abstract = "We prove that in the presence of L2 Gaussian estimates, the so-called Davies-Gaffney estimates, on-diagonal upper bounds imply precise off-diagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces.",

author = "Thierry Coulhon and Adam Sikora",

year = "2008",

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Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem

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