- Series
- Analysis Seminar
- Time
- Wednesday, March 4, 2026 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Marco Fraccaroli – University of Massachusetts Lowell – Marco_Fraccaroli@uml.edu
- Organizer
- Michael Lacey
Please Note: The Hilbert transform maps L¹ functions into weak-L¹ 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 L¹ 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.