Caltech/UCLA Joint Analysis Seminar

In this talk I will present recent work on variation-norm estimates for certain oscillatory integrals related to Carleson's theorem. The corresponding maximal operators were first studied by Stein and Wainger. Our estimates are sharp in the range of exponents, up to endpoints. The proof relies on local smoothing estimates for a family of Schrödinger-like equations due to Rogers and Seeger and square function estimates for these equations due to Lee, Rogers and Seeger. This is joint work with Shaoming Guo and Po-Lam Yung.