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Local restriction theorem and maximal Bochner-Riesz operator for the Dunkl transforms

Presented by: 
Wenrui Ye The University of International Business and Economics - Beijing
Tuesday 19th February 2019 - 15:30 to 16:05
INI Seminar Room 1

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.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons