Analysis Seminar

The classical Carleson operator, which is intimately related to the Fourier transform, was an oscillatory singular integral operator with a linear phase. Motivated by a question of Eli Stein, recent consideration of Carleson operators has focused on operators with higher degree polynomial phases. In this talk we will consider how the behavior of such polynomial Carleson operators interacts with integrating over a lower-dimensional submanifold, such as a paraboloid.