Abstract. The definition of the class of sequences of rest bounded variation is extended in order to get a wider class of sequences. The new class is not anymore a subclass of the class of quasi monotone sequences. Namely a sequence of the new class may have infinitely many zero and negative terms. Two embedding theorems proved in [2] are generalized in such a way that the new results maintain the former embedding relations but now the coefficients of the sine series belong to the new class.

AMS Subject Classification (1991): 26A15, 42A10

Received January 21, 2004. (Registered under 5859/2009.)