Analysis Seminar

Gennady UraltsevCornell Univeristy
Lebesgue points of the Fourier transform of a function and a maximal restriction estimate along variable directions.

Monday, February 26, 2018 - 2:30pm
Malott 406

We discuss the result [1] of Müller, Ricci, Wright about the nature of the Lebesgue points of the Fourier transform of an $L^p$ function and in particular if Fourier restriction to convex curves holds in the sense of Lebesgue differentiation. To do so we must study a maximal-type restriction operator.

We will show the boundedness of this operator in a slightly more general setting than initially considered in [1].

[1] Müller, D., Ricci, F., & Wright, J. (2016). A maximal restriction theorem and Lebesgue points of functions in F (L^ p). arXiv preprint