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SUMMARY:Local restriction theorem and maximal Bochner-Riesz operator for t
 he Dunkl transforms - Wenrui Ye (The University of International Business 
 and Economics - Beijing)
DTSTART:20190219T153000Z
DTEND:20190219T160500Z
UID:TALK120028@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk\, I will mainly describe joint work with Dr. Feng
  Dai on the critical index for the almost everywhere convergence of the Bo
 chner-Riesz means in weighted Lp-spaces with p=1 or p>2. Our results under
  the case p>2 are in full analogy with the classical result of M. Christ o
 n estimates of the maximal Bochner-Riesz means of Fourier integrals and th
 e classical result of A. Carbery\, Jos&eacute\; L. Rubio De Francia and L.
  Vega on a.e. convergence of Fourier integrals. Besides\, I will also intr
 oduce several new results that are related to our main results\, including
 : (i) local restriction theorem for the Dunkl transform which is significa
 ntly stronger than the global one\, but more difficult to prove\; (ii) the
  weighted Littlewood Paley inequality with Ap-weights in the Dunkl non-com
 mutative setting\; (iii) sharp local point-wise estimates of several impor
 tant kernel functions.
LOCATION:Seminar Room 1\, Newton Institute
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