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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 2, Pages 386–398 (Mi izv2253)  

This article is cited in 8 scientific papers (total in 8 papers)

Necessary and sufficient conditions for the imbedding of some classes of functions

È. A. Storozhenko


Abstract: Necessary and sufficient conditions are found for membership of a function $f(x)\in L^p(0,1)$ in the class $L^q\Phi (L)$, $1\le p\le q<\infty$. A connection is established between the modulus of continuity $\omega(\delta,f^*)$ and, on the one hand, the Fourier coefficients $a_n(f^*)$ and $b_n(f^*)$, and on the other hand the modulus of continuity $\omega(\delta,f)$.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:2, 388–400

Bibliographic databases:

UDC: 517.5
MSC: Primary 46E35; Secondary 26A15, 42A16
Received: 27.07.1971

Citation: È. A. Storozhenko, “Necessary and sufficient conditions for the imbedding of some classes of functions”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 386–398; Math. USSR-Izv., 7:2 (1973), 388–400

Citation in format AMSBIB
\Bibitem{Sto73}
\by \`E.~A.~Storozhenko
\paper Necessary and sufficient conditions for the imbedding of some classes of functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 2
\pages 386--398
\mathnet{http://mi.mathnet.ru/izv2253}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=333704}
\zmath{https://zbmath.org/?q=an:0258.46035}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 2
\pages 388--400
\crossref{https://doi.org/10.1070/IM1973v007n02ABEH001943}


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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. È. A. Storozhenko, “Embedding theorems and best approximations”, Math. USSR-Sb., 26:2 (1975), 213–224  mathnet  crossref  mathscinet  zmath
    2. V. I. Kolyada, “On imbedding in classes $\varphi(L)$”, Math. USSR-Izv., 9:2 (1975), 395–413  mathnet  crossref  mathscinet  zmath
    3. È. A. Storozhenko, “On a problem of Hardy-Littlewood”, Math. USSR-Sb., 47:2 (1984), 557–577  mathnet  crossref  mathscinet  zmath
    4. V. I. Kolyada, “Estimates of rearrangements and imbedding theorems”, Math. USSR-Sb., 64:1 (1989), 1–21  mathnet  crossref  mathscinet  zmath
    5. V. I. Kolyada, “Rearrangements of functions and embedding theorems”, Russian Math. Surveys, 44:5 (1989), 73–117  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. M. Stokolos, “Differentiation of integrals by bases without the density property”, Sb. Math., 187:7 (1996), 1061–1085  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. V. A. Andrienko, “Embedding of $H_p^\omega$ in the class $e^L$”, Russian Math. (Iz. VUZ), 54:3 (2010), 1–6  mathnet  crossref  mathscinet  elib
    8. Kolyada V.I., “Embedding Theorems For Sobolev and Hardy-Sobolev Spaces and Estimates of Fourier Transforms”, Ann. Mat. Pura Appl., 198:2 (2019), 615–637  crossref  mathscinet  zmath  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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