Arkiv för Matematik
- Ark. Mat.
- Volume 39, Number 2 (2001), 283-309.
Reverse hypercontractivity over manifolds
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 μt≡(exptX)*μ are absolutely continuous with respect to μ, it is of interest to establish bounds on the Lp (μ) norm of the Radon-Nikodym derivative dμt/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 Cm and on the Riemann surface for z1/n.
Research supported in part by CONACyT, Mexico, grant 32725-E.
Research supported in part by CONACyT, Mexico, grant 32146-E.
Ark. Mat., Volume 39, Number 2 (2001), 283-309.
Received: 25 April 2000
First available in Project Euclid: 31 January 2017
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2001 © Institut Mittag-Leffler
Galaz-Fontes, Fernando; Gross, Leonard; Sontz, Stephen Bruce. Reverse hypercontractivity over manifolds. Ark. Mat. 39 (2001), no. 2, 283--309. doi:10.1007/BF02384558. https://projecteuclid.org/euclid.afm/1485898733