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Trudy Mat. Inst. Steklova, 2003, Volume 243, Pages 87–95 (Mi tm422)  

This article is cited in 23 scientific papers (total in 23 papers)

Equivalent Normings of Spaces of Functions of Variable Smoothness

O. V. Besov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: For the Banach spaces $B_{p,q}^a$ and $F_{p,q}^a$ of functions defined on $\mathbb R^n$ whose variable smoothness $a=a(x)$ is determined by the behavior of their differences, equivalent normings are established in terms of weighted norms of smooth dyadic decompositions of their Fourier transforms.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2003, 243, 80–88

Bibliographic databases:
UDC: 517.518.23
Received in April 2003

Citation: O. V. Besov, “Equivalent Normings of Spaces of Functions of Variable Smoothness”, Function spaces, approximations, and differential equations, Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS, Trudy Mat. Inst. Steklova, 243, Nauka, MAIK Nauka/Inteperiodika, M., 2003, 87–95; Proc. Steklov Inst. Math., 243 (2003), 80–88

Citation in format AMSBIB
\Bibitem{Bes03}
\by O.~V.~Besov
\paper Equivalent Normings of Spaces of Functions of Variable Smoothness
\inbook Function spaces, approximations, and differential equations
\bookinfo Collected papers. Dedicated to the 70th birthday of Oleg Vladimirovich Besov, corresponding member of RAS
\serial Trudy Mat. Inst. Steklova
\yr 2003
\vol 243
\pages 87--95
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm422}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2049464}
\zmath{https://zbmath.org/?q=an:1084.46023}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2003
\vol 243
\pages 80--88


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. “The List of Scientific Works of O. V. Besov”, Proc. Steklov Inst. Math., 243 (2003), 7–10  mathnet  mathscinet  zmath
    2. O. V. Besov, “Interpolation, Embedding, and Extension of Spaces of Functions of Variable Smoothness”, Proc. Steklov Inst. Math., 248 (2005), 47–58  mathnet  mathscinet  zmath
    3. Besov O.V., “On the interpolation, embedding, and extension of spaces of functions of variable smoothness”, Dokl. Math., 71:2 (2005), 163–167  mathnet  mathscinet  zmath  elib  elib
    4. Schneider J., “Function spaces of varying smoothness. I”, Math. Nachr., 280:16 (2007), 1801–1826  crossref  mathscinet  zmath  isi  scopus
    5. Diening L., Hästö P., Roudenko S., “Function spaces of variable smoothness and integrability”, J. Funct. Anal., 256:6 (2009), 1731–1768  crossref  mathscinet  zmath  isi  elib  scopus
    6. Kempka H., “2-microlocal Besov and Triebel-Lizorkin spaces of variable integrability”, Rev. Mat. Complut., 22:1 (2009), 227–251  crossref  mathscinet  zmath  isi  scopus
    7. Almeida A., Hästö P., “Besov spaces with variable smoothness and integrability”, J. Funct. Anal., 258:5 (2010), 1628–1655  crossref  mathscinet  zmath  isi  scopus
    8. Kempka H., “2-Microlocal Besov Spaces”, Recent Developments in Fractals and Related Fields, Applied and Numerical Harmonic Analysis, 2010, 191–201  mathscinet  isi
    9. Kempka H., Vybiral J., “Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences”, J. Fourier Anal. Appl., 18:4 (2012), 852–891  crossref  mathscinet  zmath  isi  scopus
    10. Drihem D., “Atomic Decomposition of Besov Spaces with Variable Smoothness and Integrability”, J. Math. Anal. Appl., 389:1 (2012), 15–31  crossref  mathscinet  zmath  isi  scopus
    11. 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
    12. Yang D., Zhuo C., Yuan W., “Besov-Type Spaces With Variable Smoothness and Integrability”, J. Funct. Anal., 269:6 (2015), 1840–1898  crossref  mathscinet  zmath  isi  elib  scopus
    13. Yang D. Zhuo C. Yuan W., “Triebel-Lizorkin Type Spaces With Variable Exponents”, Banach J. Math. Anal., 9:4 (2015), 146–202  crossref  mathscinet  zmath  isi  scopus
    14. Tyulenev A.I., “Besov-type spaces of variable smoothness on rough domains”, Nonlinear Anal.-Theory Methods Appl., 145 (2016), 176–198  crossref  mathscinet  zmath  isi  scopus
    15. Almeida A., Caetano A., “on 2-Microlocal Spaces With All Exponents Variable”, Nonlinear Anal.-Theory Methods Appl., 135 (2016), 97–119  crossref  mathscinet  zmath  isi  scopus
    16. Tyulenev A.I., “On various approaches to Besov-type spaces of variable smoothness”, J. Math. Anal. Appl., 451:1 (2017), 371–392  crossref  mathscinet  zmath  isi  scopus
    17. Drihem D., Hebbache W., “Boundedness of Non Regular Pseudodifferential Operators on Variable Besov Spaces”, J. Pseudo-Differ. Oper. Appl., 8:2 (2017), 167–189  crossref  mathscinet  zmath  isi  scopus
    18. Wu S.Q., Yang D.Ch., Yuan W., Zhuo C.Q., “Variable 2-Microlocal Besov-Triebel-Lizorkin-Type Spaces”, Acta. Math. Sin.-English Ser., 34:4, SI (2018), 699–748  crossref  mathscinet  zmath  isi  scopus
    19. Goncalves H.F., Kempka H., Vybiral J., “Franke-Jawerth Embeddings For Besov and Triebel-Lizorkin Spaces With Variable Exponents”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 43:1 (2018), 187–209  crossref  mathscinet  zmath  isi  scopus
    20. V. D. Kryakvin, V. S. Rabinovich, “Pseudodifferential Operators on Besov Spaces of Variable Smoothness”, Math. Notes, 104:4 (2018), 545–558  mathnet  crossref  crossref  mathscinet  isi  elib
    21. Liu Y., Zhao J., “Bilinear Fourier Multiplier Operators on Variable Triebel Spaces”, Math. Inequal. Appl., 22:2 (2019), 677–690  crossref  mathscinet  isi  scopus
    22. Drihem D., “On the Duality of Variable Triebel-Lizorkin Spaces”, Collect. Math., 71:2 (2020), 263–278  crossref  mathscinet  isi
    23. Drihem D., “Variable Triebel-Lizorkin-Type Spaces”, Bull. Malays. Math. Sci. Soc., 43:2 (2020), 1817–1856  crossref  mathscinet  isi
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