PR ] 1 3 Ju l 2 00 4 Interpolated inequalities between exponentialand Gaussian , Orlicz hypercontractivity and isoperimetry

  title={PR ] 1 3 Ju l 2 00 4 Interpolated inequalities between exponentialand Gaussian , Orlicz hypercontractivity and isoperimetry},
  author={F. Barthe and Patrick Cattiaux and Cyril Roberto},
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F -Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide criteria for these Sobolev type inequalities and for related properties. In particular, we implement in the context of probability measures the ideas of Maz’ja’s capacity theory, and present equivalent forms relating the capacity of sets to their measure. Orlicz hypercontractivity efficiently describes… CONTINUE READING
Highly Cited
This paper has 56 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.


Publications citing this paper.

57 Citations

Citations per Year
Semantic Scholar estimates that this publication has 57 citations based on the available data.

See our FAQ for additional information.


Publications referenced by this paper.
Showing 1-10 of 52 references

A new isoperimetric inequality and the concentration of measure phenomenon

  • M. Talagrand
  • In Geometric aspects of functional analysis (1989…
  • 1991
Highly Influential
10 Excerpts

A pathwise approach of some classical inequalities

  • P. Cattiaux
  • Potential Analysis, 20:361–394,
  • 2004
Highly Influential
5 Excerpts

A generalized Beckner type inequality

  • F. Y. Wang
  • Preprint
  • 2002
Highly Influential
5 Excerpts

la and K

  • R. Lata
  • Oleszkiewicz. Between Sobolev and Poincaré. in…
  • 2000
Highly Influential
12 Excerpts

Quelques remarques sur l’ultracontractivité

  • O. Kavian, G. Kerkyacharian, B. Roynette
  • J. Func. Anal., 111:155–196,
  • 1993
Highly Influential
4 Excerpts

Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities

  • O. S. Rothaus
  • J. Func. Anal., 64:296–313,
  • 1985
Highly Influential
4 Excerpts

Maz’ja. Sobolev spaces

  • V G.
  • 1985
Highly Influential
5 Excerpts

Entropy bounds and isoperimetry

  • S. G. Bobkov, B. Zegarlinski
  • Preprint,
  • 2002
Highly Influential
4 Excerpts

Similar Papers

Loading similar papers…