Embedding theorems for Sobolev spaces of numerical sequences (Q1876437)

The author studies multiweight spaces of sequences \(l_q(\mathbb Z; r)\) and \(W_\theta (\mathbb Z; \alpha, \mu)\). He obtains necessary and sufficient conditions for the embedding \(W_\theta (\mathbb Z; \alpha, \mu)\to l_q (\mathbb Z; r)\) whenever \(0\leq \theta \leq q \leq +\infty\) or \(1\leq q < \theta < +\infty\). Two-sided estimated are established for the norms of the corresponding embedding operators and necessary and sufficient conditions are found for compactness of the unit ball of the space \(W_\theta (\mathbb Z; \alpha, \mu)\) in \(l_q (\mathbb Z; r)\). This is an English translation of the author's article published in the book [\textit{S. K. Vodop'yanov} (ed.), Proceedings on Analysis and Geometry. International conference in honor of the 70th birthday of Professor Yu. G. Reshetnyak. Novosibirsk: Izdatel'stvo Instituta Matematiki (2000; Zbl 0992.46029)].