Differential weights embedding theorem in one degenerated case

The article is devoted to the study of the conditions for embedding of the space $H_p(N_0,\beta)$ to space $l_q(N_0,\rho)$, $1<q<\infty$. Here $l_q(N_0,\rho)$ is the difference analog of a weighted Lebesgue space in which the sequence plays the role of weight. Space is defined as the completion of the set of finite sequences by the norm. In order to prove the main assertion, additional conditions are imposed on the weight. What a discrete version of M. Otelbaev's averaging is an effective tool in the study of questions on difference embedding theorems, properties of difference operators, etc. Using various types of discrete averages, the questions of embedding theory of spaces with a discrete argument are investigated, as well as bilateral estimates of the norms of the embedding and estimation operators approximate numbers of the embedding operator.