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  • 1 Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary
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Our aim is to find the source why the logarithm sequences play the crucial role in the L1-convergence of sine series. We define three new classes of sequences; one of them has the character of the logarithm sequences, the other two are the extensions of the class defined by Zhou and named Logarithm Rest Bounded Variation Sequences. In terms of these classes, extended analogues of Zhou’s theorems are proved.