Open Access
October 2018 Weak boundedness of operator-valued Bochner–Riesz means for the Dunkl transform
Maofa Wang, Bang Xu, Jian Hu
Banach J. Math. Anal. 12(4): 1064-1083 (October 2018). DOI: 10.1215/17358787-2018-0012
Abstract

We consider operator-valued Bochner–Riesz means with weight function hκ2 under a finite reflection group for the Dunkl transform. We establish the maximal inequality of the weighted Hardy–Littlewood maximal function, and we apply it to the maximal inequality of operator-valued Bochner–Riesz means BRδ(hκ2;f)(x) for δ>λκ:=d12+j=1dκj. Furthermore, we also obtain the corresponding pointwise convergence theorem.

Copyright © 2018 Tusi Mathematical Research Group
Maofa Wang, Bang Xu, and Jian Hu "Weak boundedness of operator-valued Bochner–Riesz means for the Dunkl transform," Banach Journal of Mathematical Analysis 12(4), 1064-1083, (October 2018). https://doi.org/10.1215/17358787-2018-0012
Received: 25 January 2018; Accepted: 12 April 2018; Published: October 2018
Vol.12 • No. 4 • October 2018
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