## Banach Journal of Mathematical Analysis

### Weak boundedness of operator-valued Bochner–Riesz means for the Dunkl transform

Maofa Wang, Bang Xu, and Jian Hu

#### Abstract

We consider operator-valued Bochner–Riesz means with weight function $h_{\kappa}^{2}$ 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 $B^{\delta}_{R}(h^{2}_{\kappa};f)(x)$ for $\delta\gt \lambda_{\kappa}:=\frac{d-1}{2}+\sum_{j=1}^{d}\kappa_{j}$. Furthermore, we also obtain the corresponding pointwise convergence theorem.

#### Article information

Source
Banach J. Math. Anal., Volume 12, Number 4 (2018), 1064-1083.

Dates
Accepted: 12 April 2018
First available in Project Euclid: 11 September 2018

https://projecteuclid.org/euclid.bjma/1536653147

Digital Object Identifier
doi:10.1215/17358787-2018-0012

Mathematical Reviews number (MathSciNet)
MR3858761

Zentralblatt MATH identifier
06946303

#### Citation

Wang, Maofa; Xu, Bang; Hu, Jian. Weak boundedness of operator-valued Bochner–Riesz means for the Dunkl transform. Banach J. Math. Anal. 12 (2018), no. 4, 1064--1083. doi:10.1215/17358787-2018-0012. https://projecteuclid.org/euclid.bjma/1536653147

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