Interpolation sets for Hardy-Sobolev spaces on the boundary of the unit ball of ${\bf C}^n$

Details Interpolation sets for Hardy-Sobolev spaces on the boundary of the unit ball of ${\bf C}^n$ Interpolation sets for Hardy-Sobolev spaces on the boundary of the unit ball of ${\bf C}^n$

1998-04-23

arxiv.org/abs/math/9804112v1

Mathematics

Complex Variables

LaTeX2e, 38 pages

Scientific paper

We study the interpolation sets for the Hardy-Sobolev spaces defined on the unit ball of ${\bf C}^n$. We begin by giving a natural extension to ${\bf C}^n$ 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.

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