1998/04/23 by Jaume Gudayol, Gudayol, Jaume
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #Holomorphic and Operator Theory #math.CV #msc:32A40
paper · pdf · doi:10.48550/arxiv.math/9804112
LaTeX2e, 38 pages
arxiv created 1998/04/23 · arxiv updated 2009/11/30
We study the interpolation sets for the Hardy-Sobolev spaces defined on the unit ball of \bf Cn. We begin by giving a natural extension to \bf Cn of the condition that is known to be necessay and sufficient for interpolation sets lying on the boundary of the unit disc. We show that under this condition the restriction of a function in the Hardy-Sobolev space to the set always exists, and lies in a Besov space. We then show that under the assumption that there is an holomorphic distance function for the set, there is an extension operator from these spaces to the Hardy-Sobolev ones.