Caltech/UCLA Joint Analysis Seminar

The study of the Carleson operator originally arose in the context of

the convergence of Fourier series. More recently a question of Stein expanded consideration

to Carleson operators with polynomial phases; such operators have now been successfully treated

by Victor Lie in the one-dimensional case, and in higher dimensions (under the significant restriction that

the polynomial phase has no linear term) by Stein and Wainger. One can furthermore consider Carleson operators with

polynomial phases that integrate over curves and surfaces, rather than over the full Euclidean space. This talk will

survey some recent results for such operators,

including joint work with Po-Lam Yung; with Shaoming Guo, Joris Roos, and Po-Lam Yung; and with Tess Anderson.