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Noncommutative pointwise convergence of orthogonal expansions of several variables

Author

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  • Changbao Pang
  • Maofa Wang
  • Bang Xu

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.

Suggested Citation

  • Changbao Pang & Maofa Wang & Bang Xu, 2021. "Noncommutative pointwise convergence of orthogonal expansions of several variables," Mathematische Nachrichten, Wiley Blackwell, vol. 294(8), pages 1559-1577, August.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:8:p:1559-1577
    DOI: 10.1002/mana.201900450
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