Abstract. We study the interrelation between the strong class $S_p(\lambda )$ and the Nikol'skii class $W^rH_\beta ^\omega $.

AMS Subject Classification (1991): 42A24, 42A25

Keyword(s): Strong approximation, Fourier series, Embedding theorems

Received June 16, 2005, and in revised form September 9, 2005. (Registered under 5912/2009.)