Mathematical Notes

, Volume 98, Issue 3–4, pp 550–560 | Cite as

Embedding of Sobolev space in the case of the limit exponent

Article

Abstract

We establish the embeddings of the Sobolev space Wps and the space Bpqs (in the case of the limit exponent) in the spaces of locally summable functions of zero smoothness. This refines the embeddings of the Sobolev space in the Lorentz space and in the Lorentz–Zygmund space. The relationship between the Lorentz spaces and the corresponding spaces of functions of zero smoothness is established. Similar embeddings of the spaces of potentials are determined.

Keywords

Sobolev space Wps the space Bpqs locally summable function of zero smoothness Lorentz space Lorentz–Zygmund space space of potentials 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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