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Lillian Pierce : Carleson operators of Radon type

A celebrated theorem of Carleson shows that the Fourier series of an L^2 function converges pointwise almost everywhere. At the heart of this work lies an L^2 estimate for a particular type of maximal singular integral operator, which has since become known as a Carleson operator. In the past 40 years, a number of important results have been proved for generalizations of the original Carleson operator. In this talk we will introduce the Carleson operator and survey its generalizations, and then describe new joint work with Po Lam Yung on Carleson operators with a certain type of polynomial phase that also incorporate the behavior of Radon transforms.

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