108 citations · 174 across the 13 of their papers we have counts for
Showing 2010Show all
2 papers · 1 filter
math.PR2010★ 4 cited
Weighted Nash Inequalities
Dominique Bakry, François Bolley, Ivan Gentil +1
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 pres…
math.PR2010★ 32 cited
Dimension dependent hypercontractivity for Gaussian kernels
Dominique Bakry, François Bolley, Ivan Gentil
We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture r…