BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Volberg (Michigan State University) DTSTART:20210125T200000Z DTEND:20210125T210000Z DTSTAMP:20260423T021337Z UID:paw/16 DESCRIPTION:Title: Mul ti-parameter Poincaré inequality\, multi-parameter Carleson embedding: Bo x condition versus Chang--Fefferman condition\nby Alexander Volberg (M ichigan State University) as part of Probability and Analysis Webinar\n\n\ nAbstract\nCarleson embedding theorem is a building block for many singula r integral operators and the main instrument in proving ``Leibniz rule" fo r fractional derivatives (Kato--Ponce\, Kenig). It is also an essential st ep in all known ``corona theorems’’. Multi-parameter embedding is a to ol to prove more complicated Leibniz rules that are also widely used in we ll-posedness questions for various PDEs. Alternatively\, multi-parameter e mbedding appear naturally in questions of embedding of spaces of analytic functions in polydisc into Lebesgue spaces with respect to a measure in th e polydisc. \n\nCarleson embedding theorems often serve as a first buildin g block for interpolation in complex space and also for corona type result s. The embedding of spaces of holomorphic functions on n-polydisc can be r educed (without loss of information) to the boundedness of weighted mult i-parameter dyadic Carleson embedding. We find the necessary and sufficie nt condition for this Carleson embedding in n-parameter case\, when n is 1\, 2\, or 3. The main tool is the harmonic analysis on graphs with cycle s. The answer is quite unexpected and seemingly goes against the well know n difference between box and Chang--Fefferman condition that was given by Carleson quilts example of 1974. I will present results obtained jointly b y Arcozzi\, Holmes\, Mozolyako\, Psaromiligkos\, Zorin-Kranich and myself. \n LOCATION:https://researchseminars.org/talk/paw/16/ END:VEVENT END:VCALENDAR