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Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces

Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces AbstractIn this paper, we present a new approach to obtaining the off-diagonal upperestimate of the heat kernel for any regular Dirichlet form without a killingpart on the doubling space. One of the novelties is that we have obtainedthe weighted L2{L^{2}}-norm estimate of the survival function 1-PtB⁢1B{1-P_{t}^{B}1_{B}}for any metric ball B, which yields a nice tail estimate of the heatsemigroup associated with the Dirichlet form. The parabolic L2{L^{2}} mean-valueinequality is borrowed to use. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces

Forum Mathematicum , Volume 34 (1): 53 – Jan 1, 2022

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Publisher
de Gruyter
Copyright
© 2022 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2021-0096
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper, we present a new approach to obtaining the off-diagonal upperestimate of the heat kernel for any regular Dirichlet form without a killingpart on the doubling space. One of the novelties is that we have obtainedthe weighted L2{L^{2}}-norm estimate of the survival function 1-PtB⁢1B{1-P_{t}^{B}1_{B}}for any metric ball B, which yields a nice tail estimate of the heatsemigroup associated with the Dirichlet form. The parabolic L2{L^{2}} mean-valueinequality is borrowed to use.

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 2022

Keywords: Heat kernel; Dirichlet form; Markov semigroups; 35K08; 31C25; 47D07

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