Integral isoperimetric transference and dimensionless Sobolev inequalities

Mario Milman; Joaquim Martín

doi:10.1007/s13163-014-0153-7

Integral isoperimetric transference and dimensionless Sobolev inequalities

Mario Milman, Joaquim Martín

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Abstract

© 2014, Universidad Complutense de Madrid. We introduce the concept of Gaussian integral isoperimetric transfer 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 Fiorenza et al. (2012) using extrapolation.

Original language	English
Pages (from-to)	359-392
Journal	Revista Matematica Complutense
Volume	28
DOIs	https://doi.org/10.1007/s13163-014-0153-7
Publication status	Published - 1 May 2015

Keywords

Extrapolation
Symmetrization
Sobolev inequalities
Isoperimetric inequalities

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10.1007/s13163-014-0153-7

https://ddd.uab.cat/record/268403

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AB - © 2014, Universidad Complutense de Madrid. We introduce the concept of Gaussian integral isoperimetric transfer 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 Lq spaces on the unit n-dimensional cube our results extend the recent inequalities that were obtained in Fiorenza et al. (2012) using extrapolation.

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KW - Symmetrization

KW - Sobolev inequalities

KW - Isoperimetric inequalities

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JO - Revista Matematica Complutense

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ER -

Integral isoperimetric transference and dimensionless Sobolev inequalities

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