International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 19, Pages 969-974
doi:10.1155/S0161171204308197

Sobolev space estimates for solutions of the equation ∂¯u=f on polycylinders

Patrick W. Darko1 and Clement H. Lutterodt2

1Department of Mathematics and Computer Science, Lincoln University, 19352, PA, USA
2Department of Mathematics, Howard University, Washington, DC 20059, USA

Received 10 August 2003

Copyright © 2004 Patrick W. Darko and Clement 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

In trying to improve Weinstock's results on approximation by holomorphic functions on certain product domains, we are led to estimates in Sobolev spaces for the ∂¯-operator on polycylinders for (γ,q)-forms. This generalizes our results for the same operator on polycylinders previously obtained, and can be applied to a number of other problems such as the Corona problem.