Integral isoperimetric transference and dimensionless Sobolev inequalities
Abstract
We introduce the concept of Gaussian integral isoperimetric transference and show how it can be applied to obtain a new class of sharp Sobolev-Poincar\'e inequalities with constants independent of the dimension. In the special case of Lq spaces on the unit n-dimensional cube our results extend the recent inequalities that were obtained in FKS using extrapolation.
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