Lp estimates for oscillatory singular integral operatros and Marcinkiewicz integral operators.

摘要

We present a study of the boundedness properties of a class of oscillatory singular integral operators of non-convolution type and the Marcinkiewicz integral operators with kernels in the Hardy space over the unit sphere and over a compact submanifold of finite type, respectively. Both the Lp estimates and the weighted Lp estimates are obtained for the oscillatory singular integral operators, and the weighted Lp estimates for the Marcinkiewicz integral operators are established. The same weight class was used to prove the weighted Lp estimates of both operators. This weight condition is similar to Muckenhoupt's Ap condition but more restrictive. Our work generalizes previously known results and introduces a new approach in solving a problem with kernels in the Hardy space over the unit sphere. Among the methods used are the Calderon-Zygmund theory and the theory of Ap weights.