Weighted Estimates for Oscillatory Singular Integrals. (3rd April 2013) - Al-Qassem, H.; Cheng, L.; Fukui, A.; Pan, Y.
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).