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Wenrui Ye (The University of International Business and Economics - Beijing)
Tuesday 19 February 2019, 15:30-16:05
Local restriction theorem and maximal Bochner-Riesz operator for the Dunkl transforms
- đ¤ Speaker: Wenrui Ye (The University of International Business and Economics - Beijing)
- đ Date & Time: Tuesday 19 February 2019, 15:30 - 16:05
- đ Venue: Seminar Room 1, Newton Institute
Abstract
In this talk, I will mainly describe joint work with Dr. Feng Dai on the critical index for the almost everywhere convergence of the Bochner-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 on estimates of the maximal Bochner-Riesz means of Fourier integrals and the classical result of A. Carbery, José L. Rubio De Francia and L. Vega on a.e. convergence of Fourier integrals. Besides, I will also introduce several new results that are related to our main results, including: (i) local restriction theorem for the Dunkl transform which is significantly stronger than the global one, but more difficult to prove; (ii) the weighted Littlewood Paley inequality with Ap-weights in the Dunkl non-commutative setting; (iii) sharp local point-wise estimates of several important kernel functions.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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