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arXiv · 1309.1980

Integral isoperimetric transference and dimensionless Sobolev inequalities

Joaquim Martin·Mario Milman
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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-Poincaré inequalities with constants independent of the dimension. In the special case of $L^{q}$ spaces on the unit $n-$dimensional cube our results extend the recent inequalities that were obtained in \cite{FKS} using extrapolation.

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Joaquim Martin, Mario Milman. 2013-09-08. Integral isoperimetric transference and dimensionless Sobolev inequalities. https://doi.org/10.1007/s13163-014-0153-7

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