加倍测度空间中的热核估计

Abstract

Abstract:

This paper shows the relationship between lower bounds and upper bounds of the heat kernel on metric spaces with doubling measure. If in addition the Dirichlet form is local, then a near-diagonal lower bound implies an on-diagonal upper bound. This paper gives the upper estimate in balls and then extends it to full spaces. Compared with previous work, the conclusion of this paper not only contains former result but reveals a more general relationship between the lower and upper bounds.

Key words: Heat kernels, Bounds estimates, Volume doubling measure

CLC Number:

O174

Dou Xiaoman. Obtaining Upper Bounds of Heat Kernels from Lower Bounds with Doubling Measure[J].Acta mathematica scientia,Series A, 2015, 35(3): 449-463.

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Obtaining Upper Bounds of Heat Kernels from Lower Bounds with Doubling Measure

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