BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Carmelo Puliatti (Euskal Herriko Unibertsitatea) DTSTART:20220413T160000Z DTEND:20220413T170000Z DTSTAMP:20260423T021304Z UID:HAeS/31 DESCRIPTION:Title: Gr adients of single layer potentials for elliptic operators with coefficient s of Dini mean oscillation-type\nby Carmelo Puliatti (Euskal Herriko U nibertsitatea) as part of Harmonic analysis e-seminars\n\n\nAbstract\nWe c onsider a uniformly elliptic operator $L_A$ in divergence form \nassociate d with a matrix $A$ with real\, bounded\, and possibly \nnon-symmetric coe fficients. If a proper $L^1$-mean oscillation of the \ncoefficients of $A$ satisfies suitable Dini-type assumptions\, we prove \nthe following: if $ \\mu$ is a compactly supported Radon measure in \n$R^{n+1}\, n\\geq 2\,$ the $L^2(\\mu)$-operator norm of the gradient of the \nsingle layer potent ial $T_\\mu$ associated with $L_A$ is comparable to the \n$L^2$-norm of th e $n$-dimensional Riesz transform $R_\\mu$\, modulo an \nadditive constant .\nThis makes possible to obtain direct generalizations of some deep \ngeo metric results\, initially proved for the Riesz transform\, which \nwere r ecently extended to $T_\\mu$ under a H\\"older continuity assumption \non the coefficients of the matrix $A$.\n\nThis is a joint work with Alejandro Molero\, Mihalis Mourgoglou\, and \nXavier Tolsa.\n LOCATION:https://researchseminars.org/talk/HAeS/31/ END:VEVENT END:VCALENDAR