Weighted Estimates for Oscillatory Singular Integrals. (3rd April 2013)

• Record Type: Journal Article
• Authors: Al-Qassem, H.; Cheng, L.; Fukui, A.; Pan, Y.
• Other Names: Fiorenza Alberto Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2013(2013)
• Publication Date: 2013-04-03
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2013/543748
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : 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 H 1 ( S n − 1 ), while such results were known previously only for kernels in L log L ( S n − 1 ), a proper subspace of H 1 ( S n − 1 ) . One of our results established a L p ( w ) → L p ( w ) bound for certain weights. At the same time, it provides a solution to an open problem in Lu (2005).