Abstract. We study the relation between the generalized Zygmund classes of functions defined by Leindler [2] and the class of functions possessing a given rate of the strong approximation by their Fourier series. Furthermore, we present sufficient conditions in terms of Fourier coefficients to ensure a given rate of this strong approximation; and these conditions are also necessary in the special case when the Fourier coefficients are all nonnegative.

AMS Subject Classification (1991): 42A10, 42A14, 42A32; 26A15, 41A25

Received August 29, 2007, and in revised form September 25, 2007. (Registered under 6454/2009.)