International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 17-20, 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
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.