Local restriction theorem and maximal Bochner-Riesz operator for the Dunkl transforms
Duration: 28 mins 2 secs
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| Description: |
Ye, W
Tuesday 19th February 2019 - 15:30 to 16:05 |
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| Created: | 2019-02-20 12:57 |
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| Collection: | Approximation, sampling and compression in data science |
| Publisher: | Isaac Newton Institute |
| Copyright: | Ye, W |
| Language: | eng (English) |
| 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.
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