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International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 3, Pages 475-484
http://dx.doi.org/10.1155/S0161171295000603

Cohomology with Lp-bounds on polycylinders

P. W. Darko and C. H. Lutterodt

Department of Mathematics, Howard University, Washington, D.C. 20059, USA

Received 8 October 1993; Revised 15 March 1994

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let Ω=Ω1×…×Ωn be a polycylinder in ℂn, that is each Ωj is bounded, non-empty and open in ℂ. The main result proved here is that, if Bp is the sheaf of germs of Lp-holomorphic functions on Ω¯ then Hq(Ω¯,Bp)=0 for q≥1. The proof of this is then used to establish a Leray's Isomorphism with Lp-bounds theorem.