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Dunford-Pettis composition operators on in several variables

Authors:	A Matheson

Institution:	Department of Mathematics, Lamar University, Beaumont, Texas 77710

Abstract:	A bounded composition operator $C_{\phi }$ on $H^{1}(B)$ , where is the unit ball in ${\mathbb{C}}^{n}$ , is Dunford-Pettis if and only if the radial limit function $\phi ^{*}$ of $\phi$ takes values on the unit sphere only on a set of surface measure zero. A similar theorem holds on bounded strongly pseudoconvex domains with smooth boundary.

Keywords:	Dunford-Pettis operator completely continuous operator composition operator Hardy space inner function strongly pseudoconvex domain

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