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SUMMARY:Marco Fraccaroli (University of Massachusetts Lowell)
DTSTART:20251021T180000Z
DTEND:20251021T190000Z
DTSTAMP:20260423T004824Z
UID:OARS/73
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/73/">En
 dpoint estimates for Fourier multipliers with Zygmund singularities</a>\nb
 y Marco Fraccaroli (University of Massachusetts Lowell) as part of OARS On
 line Analysis Research Seminar\n\n\nAbstract\nThe Hilbert transform maps $
 L^1$ functions into $L^{1\,\\infty}$ ones. In fact\, this estimate holds t
 rue for any operator $T_m$ defined by a bounded Fourier multiplier $m$ wit
 h singularity only in the origin. Tao and Wright identified the space repl
 acing $L^1$ in the endpoint estimate for $T_m$ when $m$ has singularities 
 in a lacunary set of frequencies\, in the sense of the Hörmander-Mihlin c
 ondition.\n\nIn this talk we will quantify how the endpoint estimate for $
 T_m$ for any arbitrary $m$ is characterized by the lack of additivity of i
 ts set of singularities $\\Xi(m)$ . This property of $\\Xi(m)$ is expresse
 d 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 expan
 sion playing the role of Calderón-Zygmund decomposition.\n\nThe talk is b
 ased on joint work with Bakas\, Ciccone\, Di Plinio\, Parissis\, and Vittu
 ri.\n
LOCATION:https://researchseminars.org/talk/OARS/73/
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