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Mat. Sb., 2015, Volume 206, Number 6, Pages 85–128 (Mi msb8399)  

This article is cited in 9 scientific papers (total in 9 papers)

Some new function spaces of variable smoothness

A. I. Tyulenev

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: A new Besov space of variable smoothness is introduced on which the norm is defined in terms of difference relations. This space is shown to be the trace of a weighted Sobolev space with a weight in the corresponding Muckenhoupt class. Methods of nonlinear spline approximation are applied to derive an atomic decomposition theorem for functions in a Besov space of variable smoothness. A complete description of traces on the hyperplane of a Besov space of variable smoothness and of a weighted Besov space with a weight in the corresponding Muckenhoupt class is given.
Bibliography: 27 titles.

Keywords: Muckenhoupt weights, weighted Sobolev spaces, weighted Besov spaces, Besov spaces of variable smoothness.

Funding Agency Grant Number
Russian Science Foundation 14-11-00443
This research was carried out with the financial support of the Russian Science Foundation (grant no. 14-11-00443).


DOI: https://doi.org/10.4213/sm8399

Full text: PDF file (780 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2015, 206:6, 849–891

Bibliographic databases:

UDC: 517.51
MSC: 46E35
Received: 01.07.2014 and 23.12.2014

Citation: A. I. Tyulenev, “Some new function spaces of variable smoothness”, Mat. Sb., 206:6 (2015), 85–128; Sb. Math., 206:6 (2015), 849–891

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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. A. I. Tyulenev, “Traces of weighted Sobolev spaces with Muckenhoupt weight. The case $p=1$”, Nonlinear Anal., 128 (2015), 248–272  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. I. Tyulenev, “Besov-type spaces of variable smoothness on rough domains”, Nonlinear Anal., 145 (2016), 176–198  mathnet  crossref  mathscinet  zmath  isi  scopus
    3. A. I. Tyulenev, “On various approaches to Besov-type spaces of variable smoothness”, J. Math. Anal. Appl., 451:1 (2017), 371–392  crossref  mathscinet  zmath  isi  scopus
    4. P. Koskelam T. Soto, Zhuang Wang, “Traces of weighted function spaces: dyadic norms and Whitney extensions”, Sci. China Math., 60:11 (2017), 1981–2010  crossref  mathscinet  isi  scopus
    5. H. Kempka, M. Schäfer, T. Ullrich, “General coorbit space theory for quasi-Banach spaces and inhomogeneous function spaces with variable smoothness and integrability”, J. Fourier Anal. Appl., 23:6 (2017), 1348–1407  crossref  mathscinet  zmath  isi  scopus
    6. D. Drihem, “Variable Besov spaces: continuous version”, J. Math. Study, 52:2 (2019), 178–226  crossref  mathscinet  zmath  isi
    7. D. Drihem, “On the duality of variable triebel-lizorkin spaces”, Collect. Math., 71:2 (2020), 263–278  crossref  mathscinet  zmath  isi
    8. D. Drihem, “Variable triebel-lizorkin-type spaces”, Bull. Malays. Math. Sci. Soc., 43:2 (2020), 1817–1856  crossref  mathscinet  zmath  isi
    9. E. P. Ushakova, “Spline Wavelet Decomposition in Weighted Function Spaces”, Proc. Steklov Inst. Math., 312 (2021), 301–324  mathnet  crossref  crossref  isi  elib
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