A new class of functions is introduced closely related to that of functions with bounded Tonelli variation and to the real Hardy space. For this class, conditions for integrability of the Fourier transform are established.

中文翻译：

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实数Hardy空间，多维变体和傅立叶变换的可积性

引入了一类新的函数，该函数与具有有限Tonelli变体的函数和实际的Hardy空间紧密相关。对于此类，建立了傅里叶变换可积性的条件。