Abstract. In this paper, we get a necessary and sufficient condition for sine series with monotonically decreasing cofficients to belong to some Orlicz space. Moreover, we have analogue results for cosine series.

AMS Subject Classification (1991): 42A32, 46E30

Keyword(s): Trigonometric series, Orlicz space

Received July 27, 2001, and in revised form November 22, 2001. (Registered under 2892/2009.)