For symmetric Dirichlet forms on doubling spaces, diagonal heat kernel upper bounds follow from Faber-Krahn, cutoff Sobolev, tail, and a new integrated jump condition, with a nearly sharp range of exponents.
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Stable characterization of diagonal heat kernel upper bounds for symmetric Dirichlet forms
For symmetric Dirichlet forms on doubling spaces, diagonal heat kernel upper bounds follow from Faber-Krahn, cutoff Sobolev, tail, and a new integrated jump condition, with a nearly sharp range of exponents.