On the integral modulus of continuity of Fourier series

We study L ^p -integrability (1<p?? of trigonometric series under the assumptions that the sequence of coefficients of ?? belongs to the class $overline{mathrm{GM}}_{theta}^{r}$ . Then we discuss the relations between the properties of ?? and the properties of the sequence (?? _n )??GM(??,r), and deduce an estimate for modulus of continuity of ?? in L ^p norm.