This article is cited in 4 papers

Embedding Nikol'skiĭclasses into Lorentz spaces

B. V. Simonov

Volgograd State Technical University, Volgograd, Russia

Abstract: We consider the embeddings of the Nikol'skiĭclasses of Lorentz spaces into Lorentz spaces. We obtain necessary and sufficient conditions for these embeddings under some restrictions on the fundamental functions of a Lorentz space.

Keywords: embedding of function classes, Nikol'skiĭclass, Lorentz space, continuity modulus, periodic function.

UDC: 517.5

Received: 06.06.2009

 English version: Siberian Mathematical Journal, 2010, 51:4, 728–744

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