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

P.W. Darko and C.H. Lutterodt

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

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.