Marco Fraccaroli (UMass Lowell) - Endpoint estimates for Fourier multipliers with Zygmund singular.. скачать в хорошем качестве

Marco Fraccaroli (UMass Lowell) - Endpoint estimates for Fourier multipliers with Zygmund singular..

Marco Fraccaroli (University of Massachusetts Lowell) - Endpoint estimates for Fourier multipliers with Zygmund singularities Recorded talk on Oct 21, 2025 at the Online Analysis Research Seminar (OARS) 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 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. https://sites.google.com/view/o-a-r-s