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A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces

Boutayeb, Salahaddine; Coulhon, Thierry; Sikora, Adam


On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively to the Nash inequality and to a Gagliardo-Nirenberg type inequality when the volume growth is polynomial. This yields a new proof and a generalisation of the well-known equivalence between classical heat kernel upper bounds and relative Faber-Krahn...[Show more]

CollectionsANU Research Publications
Date published: 2015
Type: Journal article
Source: Advances in Mathematics
DOI: 10.1016/j.aim.2014.08.014


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