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Revista Matemática Complutense

, Volume 28, Issue 2, pp 359–392 | Cite as

Integral isoperimetric transference and dimensionless Sobolev inequalities

  • Joaquim Martín
  • Mario Milman
Article

Abstract

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.

Keywords

Sobolev inequalities Symmetrization Isoperimetric inequalities Extrapolation 

Mathematics Subject Classification (2000)

46E30 26D10 

Notes

Acknowledgments

We are very grateful to the referees for their comments and suggestions to improve the quality of the paper.

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Copyright information

© Universidad Complutense de Madrid 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversitat Autònoma de BarcelonaBarcelonaSpain

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