Comparison inequalities for heat semigroups and heat kernels on metric measure spaces (Q709224)

The authors prove a certain inequality for a subsolution of the heat equation associated with a regular Dirichlet form. As a consequence of this inequality they obtain various interesting comparison inequalities for heat semigroups and heat kernels which are then used to obtain various pointwise estimates of the heat kernels. As an application the authors give a new proof of sub-Gaussian upper bounds of the heat kernel from on-diagonal bounds and tail estimates.