Reverse hypercontractivity over manifolds

Fernando Galaz-Fontes Centro de Investigación en Matemáticas, Guanajuato, Gto., Mexico Leonard Gross Department of Mathematics, Cornell University Stephen Bruce Sontz Universidad Autónoma Metropolitana-Iztapalapa, Mexico, DF, Mexico

TBD mathscidoc:1701.332964

Arkiv for Matematik, 39, (2), 283-309, 2000.4
Suppose that$X$is a vector field on a manifold$M$whose flow, exp$tX$, exists for all time. If μ is a measure on$M$for which the induced measures$μ$_{$t$}≡(exp$tX$)_{*}$μ$are absolutely continuous with respect to μ, it is of interest to establish bounds on the$L$^{$p$}(μ) norm of the Radon-Nikodym derivative$dμ$_{$t$}/$dμ$. We establish such bounds in terms of the divergence of the vector field$X$. We then specilize$M$to be a complex manifold and derive reverse hypercontractivity bounds and reverse logarithmic Sololev inequalities in some holomorphic function spaces. We give examples on$C$^{m}and on the Riemann surface for$z$^{1/$n$}.
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  title={Reverse hypercontractivity over manifolds},
  author={Fernando Galaz-Fontes, Leonard Gross, and Stephen Bruce Sontz},
  booktitle={Arkiv for Matematik},
Fernando Galaz-Fontes, Leonard Gross, and Stephen Bruce Sontz. Reverse hypercontractivity over manifolds. 2000. Vol. 39. In Arkiv for Matematik. pp.283-309.
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