  In this paper we obtain the necessary and sufficient conditions for embedding
results of different function classes. The main result is a criterion for
embedding theorems for the so-called generalized Weyl-Nikol'skii class and the
generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the
concept of a $(\lambda,\beta)$-derivative, which is a generalization of the
derivative in the sense of Weyl. As corollaries, we give estimates of norms and
moduli of smoothness of transformed Fourier series.
