Optimal heat kernel bounds under logarithmic Sobolev inequalities
Optimal heat kernel bounds under logarithmic Sobolev inequalities
We establish optimal uniform upper estimates on heat kernels whose generators satisfy a logarithmic Sobolev inequality (or entropy-energy inequality) with the optimal constant of the Euclidean space. Off-diagonals estimates may also be obtained with however a smaller d istance involving harmonic functions. In the last part, we apply these methods …