In this paper, the boundedness of the maximal function for an operator-valued weighted L₁ space on the unit sphere of ${\mathbb{R}}^{d+1}$, 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 ${\mathbb{Z}}_2^d$.

中文翻译：

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几个变量的正交展开的非对易逐点收敛

在本文中，单位球面上的算子加权L ₁空间的极大函数的有界性${\mathbb{电阻}}^{d+1}$，其中权函数在有限反射群下是不变的。我们用它来证明h谐波中正交展开的有界性，这个结果适用于各种求和方法。此外，我们得到了相应的逐点收敛定理。最后，我们在特殊反射组中给出了一些结果${\mathbb{Z}}_2^d$.