M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “Relations between mixed moduli of smoothness, and embedding theorems for Nikol'skii classes”, Trudy Mat. Inst. Steklova, 2010, Volume 269,Pages <nobr>204

This article is cited in 18 papers

Relations between mixed moduli of smoothness, and embedding theorems for Nikol'skii classes

M. K. Potapov^a, B. V. Simonov^b, S. Yu. Tikhonov^acd

^a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
^b Volgograd State Technical University, Volgograd, Russia
^c Centre de Recerca Matemàtica, Barcelona, Spain
^d Institució Catalana de Recerca i Estudis Avancats, Barcelona, Spain

Abstract: We prove $(L_p,L_q)$ inequalities for mixed moduli of smoothness of positive orders. As corollaries, we obtain embedding theorems for the Nikol'skii classes.

UDC: 517.5

Received in September 2009