International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 59830, 16 pages
doi:10.1155/IJMMS/2006/59830
On an extension of singular integrals along manifolds of finite type
1Department of Mathematics, An-Najah National University, P.O. Box 7, Nablus, West Bank, Palestinian Authority
2Department of Mathematics, AUniversity of Wisconsin-Milwaukee, Milwaukee 53201, WI, USA
3Huazhong Normal University of China, Wuhan 43007, China
Received 14 November 2005; Revised 9 April 2006; Accepted 25 April 2006
Copyright © 2006 Abdelnaser Al-Hasan and Dashan Fan. 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
We extend the Lp-boundedness of a class of singular integral operators
under the H1 kernel condition on a compact manifold from the homogeneous
Sobolev space L˙αp(ℝn) to the Lebesgue space
Lp(ℝn).