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Mat. Sb., 2012, Volume 203, Number 8, Pages 3–16 (Mi msb8107)  

This article is cited in 6 scientific papers (total in 6 papers)

On spaces of functions of smoothness zero

O. V. Besov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The paper is concerned with the new spaces $\overline B _{p,q}^0$ of functions of smoothness zero defined on the $n$-dimensional Euclidean space $\mathbb R^n$ or on a subdomain $G$ of $\mathbb R^n$. These spaces are compared with the spaces $B_{p,q}^0(\mathbb R^n)$ and $\mathrm{bmo}(\mathbb R^n)$. The embedding theorems for Sobolev spaces are refined in terms of the space $\overline B _{p,q}^0$ with the limiting exponent.
Bibliography: 8 titles.

Keywords: spaces of differentiable functions, embedding theorems, Sobolev spaces.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00774
10-01-91331
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Ministry of Education and Science of the Russian Federation НШ-6431.2012.1
2.1.1/12136


DOI: https://doi.org/10.4213/sm8107

Full text: PDF file (501 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:8, 1077–1090

Bibliographic databases:

UDC: 517.518.23
MSC: 46E35
Received: 23.01.2012 and 10.05.2012

Citation: O. V. Besov, “On spaces of functions of smoothness zero”, Mat. Sb., 203:8 (2012), 3–16; Sb. Math., 203:8 (2012), 1077–1090

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. V. Besov, “To the Sobolev embedding theorem for the limiting exponent”, Proc. Steklov Inst. Math., 284 (2014), 81–96  mathnet  crossref  crossref  isi  elib  elib
    2. F. Cobos, Ó. Domínguez, “On Besov spaces of logarithmic smoothness and Lipschitz spaces”, J. Math. Anal. Appl., 425:1 (2015), 71–84  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. I. Tyulenev, “Some new function spaces of variable smoothness”, Sb. Math., 206:6 (2015), 849–891  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. F. Cobos, O. Dominguez, H. Triebel, “Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups”, J. Funct. Anal., 270:12 (2016), 4386–4425  crossref  mathscinet  zmath  isi  scopus
    5. F. Cobos, O. Dominguez, “On the relationship between two kinds of Besov spaces with smoothness near zero and some other applications of limiting interpolation”, J. Fourier Anal. Appl., 22:5 (2016), 1174–1191  crossref  mathscinet  zmath  isi  scopus
    6. O. Dominguez, “Sharp Estimates of the Norms of Embeddings Between Besov Spaces”, Z. Anal. ihre. Anwend., 37:2 (2018), 127–149  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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