Convex Sobolev inequalities and spectral gap

  title={Convex Sobolev inequalities and spectral gap},
  author={Jean Dolbeault and Jean-Philippe Bartier},
This note is devoted to the proof of convex Sobolev (or generalized Poincar\'{e}) inequalities which interpolate between spectral gap (or Poincar\'{e}) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap… CONTINUE READING


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