A natural localization of Hardy spaces in several complex variables

Mihai Putinar; Roland Wolff

ArticleOriginal scientific text

Title

A natural localization of Hardy spaces in several complex variables

Authors ¹, ^2,³

Affiliations

Department of Mathematics, University of California, Riverside, California 92521, U.S.A.
Mathematisches Institut, Westfälische Wilhelms-Universität, 48149 Münster, Germany
Fachbereich Mathematik, Universität des Saarlandes, 6600 Saarbrücken, Germany

Abstract

Let H²(bΩ) be the Hardy space of a bounded weakly pseudoconvex domain in

ℂ^{n}

. The natural resolution of this space, provided by the tangential Cauchy-Riemann complex, is used to show that H²(bΩ) has the important localization property known as Bishop's property (β). The paper is accompanied by some applications, previously known only for Bergman spaces.

Keywords

ENG

weakly pseudoconvex domain, Hardy space, quasi-coherent module, Bishop's property (β), Toeplitz operators

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Title

A natural localization of Hardy spaces in several complex variables

Affiliations

Abstract

Keywords

Bibliography