International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 3, Pages 475-484
doi:10.1155/S0161171295000603
Cohomology with Lp-bounds on polycylinders
Department of Mathematics, Howard University, Washington 20059, D.C., USA
Received 8 October 1993; Revised 15 March 1994
Copyright © 1995 P. W. Darko and C. H. Lutterodt. 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.