Vol. 93, No. 2, 1981

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The sheaf of Hp-functions in product domains

Sergio Eduardo Zarantonello

Vol. 93 (1981), No. 2, 479–493
Abstract

Let W = W1 ×W2 ××Wn be a bounded polydomain in Cn such that the boundary of each Wi consists of finitely many disjoint Jordan curves. The correspondence that assigns to every relatively open polydomain V in W (the closure of W) the Hardy space p(V W), defines a sheaf Wp over W. This sheaf is locally determined in the sense that Γ(W,Wp) is canonically isomorphic to p(W). In this paper we prove, for any 0 < p < and all integers q 1, that the cohomology groups Hq(W,Wp) are trivial.

Mathematical Subject Classification 2000
Primary: 32A35
Secondary: 32C35, 46J15
Milestones
Received: 19 June 1978
Revised: 30 October 1978
Published: 1 April 1981
Authors
Sergio Eduardo Zarantonello