Interpolation and Sampling Hypersurfaces for weighted Bergman spaces on the unit ball

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dc.creatorForgacs, Tamas
dc.creatorVarolin, Dror
dc.date2005-04-12
dc.date2006-07-13
dc.date.accessioned2026-07-07T06:39:46Z
dc.date.available2026-07-07T06:39:46Z
dc.descriptionWe present sufficient conditions on a smooth uniformly flat hypersurface W in the unit ball to be an interpolation hypersurface or a sampling hypersurface for generalized Bergman spaces associated to the unit ball with its Bergman metric. The conditions are phrased in terms of a geometric Beurling-type densities, similar to the densities defined for hypersurfaces in C^n by Ortega-Cerda, Schuster and the second author. For the case of sampling, our proofs are different than those in the C^n case; we use an approach closer in spirit to the work of Berndtsson and Ortega-Cerda in the 1-dimensional case. For the case of interpolation we use a modified version of the Ohsawa-Takegoshi method to carry out the interpolation in the situation where the density of W is a little less than optimal. For the general case, we use the same approach as in the C^n case, except that we use an improved dbar theorem, due to Ohsawa, to solve our Cousin problem with L^2 bounds. As in the case of C^n, it is expected that our sufficient conditions are also necessary.
dc.descriptionFinal Version. To appear in International Journal of Mathematics
dc.identifierhttps://arxiv.org/abs/math/0504252
dc.identifierhttp://arxiv.org/abs/math/0504252
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101201
dc.subjectComplex Variables
dc.subject32A36
dc.titleInterpolation and Sampling Hypersurfaces for weighted Bergman spaces on the unit ball
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