# A degree one Carleson operator along the paraboloid

## Speaker:

## Institution:

## Time:

## Location:

Carleson proved in 1966 that the Fourier series of any square integrable

function converges pointwise almost everywhere to the function, by establishing boundedness

of the maximally modulated Hilbert transform from L^2 into weak L^2. This

talk is about a generalization of his result, where the Hilbert transform

is replaced by a singular integral operator along a paraboloid. I will

review the history of extensions of Carleson's theorem, and then discuss

the two main ingredients needed to deduce our result: sparse bounds for

singular integrals along the paraboloid, and a square function argument

relying on the geometry of the paraboloid.