Heat kernel lower Gaussian estimates in the doubling setting without Poincaré inequality
Heat kernel lower Gaussian estimates in the doubling setting without Poincaré inequality
In the setting of a manifold with doubling property satisfying a Gaussian upper estimate of the heat kernel, one gives a characterization of the lower Gaussian estimate in terms of certain Hölder inequalities. ContentsIntroduction 457 1. Assumptions 461 2. Preliminaries 462 3. Hölder continuity of the heat kernel 462 4. …