Parabolic mean value inequality and on-diagonal upper bound of the heat kernel on doubling spaces
Grigoryan, Alexander
Grigoryan
Alexander
Hu, Eryan
Hu
Eryan
Hu, Jiaxin
Hu
Jiaxin
We prove the diagonal upper bound of heat kernels for regular Dirichlet forms on metric measure spaces with volume doubling condition. As hypotheses, we use the Faber-Krahn inequality, the generalized capacity condition and an upper bound for the integrated tail of the jump kernel. The proof goes though a parabolic mean value inequality for subcaloric functions.
Springer
2023