The main theorem of this paper establishes a necessary and sufficient condition for embedding Schramm spaces $$\varPhi BV$$ into Chanturiya classes $$V[\nu ]$$ . This result is new even for the classical spaces in the theory of Fourier series, namely, for the Wiener and the Salem classes. Furthermore, it provides a characterization of the embedding of Waterman classes $$\varLambda BV$$ into $$V[\nu ]$$ . As a by-product of the main result, we establish a convergence criterion for the Fourier series of functions of $$\varPhi BV$$ ; this is an extension of a well-known result due to Salem. An estimate on the magnitude of the Fourier coefficients in the space $$\varPhi BV$$ is also given, and finally it is shown that some of these results can be extended to a more general setting.

中文翻译：

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将 Schramm 空间嵌入 Chanturiya 类

本文的主要定理建立了将 Schramm 空间 $$\varPhi BV$$ 嵌入 Chanturiya 类 $$V[\nu ]$$ 的充分必要条件。即使对于傅立叶级数理论中的经典空间，即 Wiener 和 Salem 类，这个结果也是新的。此外，它还提供了 Waterman 类 $$\varLambda BV$$ 嵌入 $$V[\nu ]$$ 的特征。作为主要结果的副产品，我们为 $$\varPhi BV$$ 的傅立叶级数函数建立了收敛标准；这是由于塞勒姆的众所周知的结果的扩展。还给出了对空间 $$\varPhi BV$$ 中傅立叶系数大小的估计，最后表明其中一些结果可以扩展到更一般的设置。