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Mat. Zametki, 2017, Volume 101, Issue 4, Pages 503–515 (Mi mz11369)  

Another Note on the Embedding of the Sobolev Space for the Limiting Exponent

O. V. Besov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The embedding of the Sobolev spaces $W_p^s(\mathbb{R}^n)$ in a Lizorkin-type space of locally summable functions of zero smoothness is established. This result is extended to the case of the embedding of Sobolev spaces on nonregular domains of $n$-dimensional Euclidean space. The formulation of the theorem depends on the geometric parameters of the domain of the functions.

Keywords: Sobolev space, Lizorkin space, embedding theorem, zero smoothness.

Funding Agency Grant Number
Russian Science Foundation 14-11-00443
This work was supported by the Russian Science Foundation under grant 14-11-00443.


DOI: https://doi.org/10.4213/mzm11369

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English version:
Mathematical Notes, 2017, 101:4, 608–618

Bibliographic databases:

UDC: 517.518.23
Received: 07.09.2016
Revised: 06.10.2016

Citation: O. V. Besov, “Another Note on the Embedding of the Sobolev Space for the Limiting Exponent”, Mat. Zametki, 101:4 (2017), 503–515; Math. Notes, 101:4 (2017), 608–618

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