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Journal of Function Spaces and Applications
Volume 2013, Article ID 543748, 3 pages
Research Article

Weighted Estimates for Oscillatory Singular Integrals

1Department of Mathematics and Physics, Qatar University, Doha, Qatar
2Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, USA
3Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Received 25 January 2013; Accepted 15 March 2013

Academic Editor: Alberto Fiorenza

Copyright © 2013 H. Al-Qassem et al. 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.


We establish uniform bounds for oscillatory singular integrals as well as oscillatory singular integral operators. We allow the singular kernel to be given by a function in the Hardy space , while such results were known previously only for kernels in log , a proper subspace of . One of our results established a bound for certain weights. At the same time, it provides a solution to an open problem in Lu (2005).