Events
DMS Analysis and Stochastic Analysis Seminar (SASA) |
| Time: Mar 02, 2026 (02:00 PM) |
| Location: 328 Parker Hall |
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Details:  Speaker: Marco Fraccaroli (University of Massachusetts Lowell)
Title: Endpoint estimates for Fourier multipliers with Zygmund singularities
Abstract: 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 of 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.
Host: Bingyang Hu
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