The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set \(W\subset\mathbb{R}_+^n\) containing the intersection of some neighborhood of the origin with \(\mathbb{R}_+^n\). It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln⁺L)ⁿ⁻¹.

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关于多重傅里叶-哈尔级数的几乎所有位置的收敛

本文研究了多个傅里叶-哈尔级数的收敛性问题，其中部分和取自给定凸有界集\（W \ subset \ mathbb {R} _ + ^ n \）的相似副本，其中包含以\（\ mathbb {R} _ + ^ n \）为原点。证明了对于具有对称结构的这种类型的集合W，几乎可以保证L（ln ⁺ L）^{n -1}类中任何函数的Fourier-Haar级数的收敛性。