In this paper, the properties of Lipschitz functions are considered and the convergence of the special type of series of Fourier coefficients with respect to general orthonormal systems (ONS) is investigated. For the functions of ONS we find a condition under which the special series of Fourier coefficients of Lipschitz functions with respect to general orthonormal systems are convergent. The obtained results indicate that the character of classical ONS (trigonometric, Haar, Walsh systems) and of the general ONS are different in the general case. In addition, a result on subsequences of general ONS is given.

中文翻译：

---

Lipschitz函数的一般傅里叶系数的一些性质

在本文中，考虑了 Lipschitz 函数的性质，并研究了特殊类型的傅立叶系数系列相对于一般正交系统 (ONS) 的收敛性。对于 ONS 的函数，我们找到了一个条件，在该条件下，Lipschitz 函数的傅里叶系数的特殊级数相对于一般正交系统是收敛的。得到的结果表明经典ONS（三角、Haar、Walsh系统）和一般ONS在一般情况下的特征是不同的。此外，给出了一般ONS的子序列的结果。