Sharp bilinear estimates for singular integral operators and their maximal counterparts with kernels in weighted spaces

by Dr Stefanos Lappas (University of Bonn)

Friday May 15, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60, Seminarraum 0.011 (Mathezentrum)

We discuss the boundedness properties of bilinear singular integral operators (including their maximal versions) associated with rough homogeneous kernels on $\mathbb{R}$. In particular, we focus on the $L^{p_1}(\mathbb{R}) \times L^{p_2}(\mathbb{R}) \to L^p(\mathbb{R})$ bounds in the optimal quasi-Banach range of exponents $1<p_1, p_2<\infty$ and $1/2<p<\infty$, when the angular component $\Omega$ of the kernel belongs to weighted $L^q$-spaces on the unit sphere $\mathbb{S}^1$ and has vanishing integral. This talk is based on two joint works with Petr Honzík, Lenka Slavíková and Bae Jun Park.