Kristian Seip: Critical exponents for the Riesz projection

Abstract:

We study the Riesz projection on \(\mathbb T^d\) for \(d\ge 1\) and are interested in knowing when it is a contraction from \(L^q\) to \(L^p\). The critical exponent for a given \(q\) is the largest \(p\) for which contractivity holds. I will try to motivate this problem and explain what is known, and what we are unable to prove but expect to be true. The talk is based on a joint paper with H. Queffélec, S. Konyagin, and E. Saksman as well as work in progress with O. Brevig and A. Llinares.