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Noncommutative pointwise convergence of orthogonal expansions of several variables
Author(s) -
Pang Changbao,
Wang Maofa,
Xu Bang
Publication year - 2021
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900450
Subject(s) - mathematics , pointwise , pointwise convergence , pure mathematics , unit sphere , noncommutative geometry , invariant (physics) , mathematical analysis , mathematical physics , approx , computer science , operating system
In this paper, the boundedness of the maximal function for an operator‐valued weighted L 1 space on the unit sphere of R d + 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 Z 2 d .