Noncommutative pointwise convergence of orthogonal expansions of several variables

Changbao Pang, Maofa Wang and Bang Xu

Mathematische Nachrichten, 2021, vol. 294, issue 8, 1559-1577

Abstract: In this paper, the boundedness of the maximal function for an operator‐valued weighted L1 space on the unit sphere of Rd+1, in which the weight functions are invariant under finite reflection groups, is established. We use it to prove the boundedness of orthogonal expansions in h‐harmonics and this result applies to various methods of summability. Furthermore, we obtain the corresponding pointwise convergence theorems. At last, we give some results in the special reflection group Z2d.

Date: 2021
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