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

  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},
  • F. Dai, Wenrui Ye
  • 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… 
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