Abstract
Suppose thatX is a vector field on a manifoldM whose flow, exptX, exists for all time. If μ is a measure onM for which the induced measuresμ t ≡(exptX)* μ are absolutely continuous with respect to μ, it is of interest to establish bounds on theL p (μ) norm of the Radon-Nikodym derivativedμ t /dμ. We establish such bounds in terms of the divergence of the vector fieldX. We then specilizeM to be a complex manifold and derive reverse hypercontractivity bounds and reverse logarithmic Sololev inequalities in some holomorphic function spaces. We give examples onC m and on the Riemann surface forz 1/n.
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Research supported in part by CONACyT, Mexico, grant 32725-E.
Research supported in part by CONACyT, Mexico, grant 32146-E.
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Galaz-Fontes, F., Gross, L. & Sontz, S.B. Reverse hypercontractivity over manifolds. Ark. Mat. 39, 283–309 (2001). https://doi.org/10.1007/BF02384558
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DOI: https://doi.org/10.1007/BF02384558