Banach Journal of Mathematical Analysis

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

Maofa Wang, Bang Xu, and Jian Hu

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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.

Article information

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

Dates
Received: 25 January 2018
Accepted: 12 April 2018
First available in Project Euclid: 11 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1536653147

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

Mathematical Reviews number (MathSciNet)
MR3858761

Zentralblatt MATH identifier
06946303

Subjects
Primary: 46L52: Noncommutative function spaces 32C05: Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]

Keywords
Dunkl transform von Neumann algebra Bochner–Riesz means

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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