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| | If you are a biologist and want to get the best out of the powerful methods of modern computational statistics, this is your book.
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| In this lecture, we studySobolev inequalities on Dirichlet spaces. The approach we develop is related to Hardy-Littlewood-Sobolev theory The link between the Hardy-Littlewood-Sobolev theory and heat kernel upper bounds is due to Varopoulos, but the proof I give below I learnt it from my colleague RodrigoBaƱuelos. It bypasses the Marcinkiewicz interpolation theorem,that was originally used...