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Article Dans Une Revue Revista Matemática Iberoamericana Année : 2012

Weighted Nash Inequalities


Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this work we present a simple and extremely general method, based on weighted Nash inequalities, to obtain non-uniform bounds on the kernel densities. Such bounds imply a control on the trace or the Hilbert-Schmidt norm of the heat kernels. We illustrate the method on the heat kernel on $\dR$ naturally associated with the measure with density $C_a\exp(-|x|^a)$, with $1
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Dates et versions

hal-00474543 , version 1 (20-04-2010)
hal-00474543 , version 2 (24-06-2010)



Dominique Bakry, François Bolley, Ivan Gentil, Patrick Maheux. Weighted Nash Inequalities. Revista Matemática Iberoamericana, 2012, 28 (3), pp.879-906. ⟨10.4171/RMI/695⟩. ⟨hal-00474543v2⟩
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