- Marco Fraccaroli
- Postdoc
- University of Massachusetts Lowell
- Date: March 02, Monday, 2026
- Time: 14:00-14:50
- Host: Bingyang Hu
- Room: Parker 328
- Abstract: The Hilbert transform maps \(L^1\) functions into weak-\(L^1\) ones. In fact, this estimate holds true for any operator \(T(m)\) defined by a bounded Fourier multiplier \(m\) with singularity only in the origin. Tao and Wright identified the space replacing \(L^1\) in the endpoint estimate for \(T(m)\) when \(m\) has singularities in a lacunary set of frequencies, in the sense of the Hörmander-Mihlin condition. In this talk we will quantify how the endpoint estimate for \(T(m)\) for any arbitrary \(m\) is characterized by the lack of additivity of its set of singularities. This property of the set of singularities of \(m\) is expressed in terms of a Zygmund-type inequality. The main ingredient in the proof of the estimate is a multi-frequency projection lemma based on Gabor expansion playing the role of Calderón-Zygmund decomposition. The talk is based on joint work with Bakas, Ciccone, Di Plinio, Parissis, and Vitturi.