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SUMMARY:Loredana Lanzani (Syracuse University)
DTSTART:20210331T160000Z
DTEND:20210331T170000Z
DTSTAMP:20260423T052642Z
UID:HAeS/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HAeS/13/">Th
 e commutator of the Cauchy-Szegő projection for domains in $C^n$ with min
 imal smoothness</a>\nby Loredana Lanzani (Syracuse University) as part of 
 Harmonic analysis e-seminars\n\n\nAbstract\nLet $D\\subset\\C^n$ be a boun
 ded\, strongly pseudoconvex domain whose boundary $bD$ satisfies the minim
 al regularity condition of class $C^2$.\nWe characterize boundedness and c
 ompactness in $L^p(bD\, \\omega)$\,\, for $1< p < \\infty$\,of the commuta
 tor $[b\,S_\\omega]$ where $S_\\omega$ is the Cauchy--Szegő (orthogonal) 
 projection  of  $L^2(bD\, \\omega)$ onto the holomorphic Hardy space $H^2(
 bD\, \\omega)$\n   and the measure $\\omega$  belongs to a family  (the ``
 Leray Levi-like'' measures)\n that includes induced Lebesgue measure $\\si
 gma$.  We next consider a much larger family of measures $\\{\\Omega_p\\}$
  modeled after the Muckenhoupt $A_p$-weights for $\\sigma$:\n we define th
 e holomorphic Hardy spaces $H^p(bD\, \\Omega_p)$ and we characterize\n bou
 ndedness and compactness of $[b\, S_{\\Omega_2}]$ in $L^2(bD\, \\Omega_2)$
 .\n Earlier closely related results rely upon an asymptotic expansion\, an
 d subsequent pointwise estimates\, of the Cauchy--Szegő kernel that are n
 ot available in the settings of minimal regularity {of $bD$} and/or $A_p$-
 like measures. \n\n\n  \n  This is joint work with Xuan Thinh Duong\, Ji L
 i and Brett D. Wick.\n
LOCATION:https://researchseminars.org/talk/HAeS/13/
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