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

@article{Dai2018LocalRT,
title={Local restriction theorem and maximal Bochner-Riesz operators for the Dunkl transforms},
author={Feng Dai and Wenrui Ye},
journal={Transactions of the American Mathematical Society},
year={2018}
}
• Published 26 June 2018
• Mathematics
• Transactions of the American Mathematical Society
For the Dunkl transforms associated with the weight functions hκ(x) = ∏d j=1 |xj |j , κ1, · · · , κd ≥ 0 on Rd, it is proved that if p ≥ 2 + 1 λκ and λκ := d−1 2 + ∑d j=1 κj , the maximal Bochner-Riesz operator B δ ∗(h 2 κ; f) order δ > 0 is bounded on the space L(R;hκdx) if and only if δ > δκ(p) := max{(2λκ +1)( 1 2 − 1 p )− 1 2 , 0}. This extends a well known result of M. Christ for the classical Fourier transforms (Proc. Amer. Math. Soc. 95 (1985), 16–20). The proof relies on a new local…
2 Citations
Almost everywhere convergence of the Bochner–Riesz means for the Dunkl transforms of weighted $$L^{p}$$-functions
For the Dunkl transforms associated with the weight functions $$h_{\kappa }^2(x)=\prod _{j=1}^d |x_j|^{2{\kappa }_j}$$ , $${\kappa }_1,\ldots , {\kappa }_d\ge 0$$ on $${{\mathbb {R}}}^d$$ , it is

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