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Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 2, Pages 418–437 (Mi izv1837)  

This article is cited in 10 scientific papers (total in 10 papers)

On imbedding in classes $\varphi(L)$

V. I. Kolyada


Abstract: In this paper necessary and sufficient conditions are found for imbeddings of the form $H_p^{\omega_1,…,\omega_k}\subset L^p\Phi(L)$. It is proved that in the one-dimensional case the corresponding condition on the modulus of continuity of a monotone function $f\in L^p(0,1)$ is not only sufficient but also necessary for $f\in L^p\Phi(L)$. In connection with this the existence is established of a monotone function in $L^p$ with preassigned order of modulus of continuity.
Bibliography: 10 items.

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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:2, 395–413

Bibliographic databases:

UDC: 517.5
MSC: Primary 46E35; Secondary 41A63, 26A15
Received: 30.01.1974

Citation: V. I. Kolyada, “On imbedding in classes $\varphi(L)$”, Izv. Akad. Nauk SSSR Ser. Mat., 39:2 (1975), 418–437; Math. USSR-Izv., 9:2 (1975), 395–413

Citation in format AMSBIB
\Bibitem{Kol75}
\by V.~I.~Kolyada
\paper On imbedding in classes~$\varphi(L)$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 2
\pages 418--437
\mathnet{http://mi.mathnet.ru/izv1837}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=374888}
\zmath{https://zbmath.org/?q=an:0314.46031}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 2
\pages 395--413
\crossref{https://doi.org/10.1070/IM1975v009n02ABEH001483}


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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. V. I. Kolyada, “On embedding in classes of continuous functions of several variables”, Math. USSR-Sb., 28:3 (1976), 377–388  mathnet  crossref  mathscinet  zmath  isi
    2. V. I. Kolyada, “Imbedding theorems and inequalities in various metrics for best approximations”, Math. USSR-Sb., 31:2 (1977), 171–189  mathnet  crossref  mathscinet  zmath  isi
    3. V. I. Kolyada, “On the essential continuity of summable functions”, Math. USSR-Sb., 36:3 (1980), 301–322  mathnet  crossref  mathscinet  zmath  isi
    4. È. A. Storozhenko, “On a problem of Hardy-Littlewood”, Math. USSR-Sb., 47:2 (1984), 557–577  mathnet  crossref  mathscinet  zmath
    5. V. I. Kolyada, “Estimates of rearrangements and imbedding theorems”, Math. USSR-Sb., 64:1 (1989), 1–21  mathnet  crossref  mathscinet  zmath
    6. V. I. Kolyada, “Rearrangements of functions and embedding theorems”, Russian Math. Surveys, 44:5 (1989), 73–117  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. M. Stokolos, “On the strong differentiation of integrals of functions from Hölder classes”, Math. Notes, 55:1 (1994), 57–70  mathnet  crossref  mathscinet  zmath  isi
    8. 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
    9. B. V. Simonov, “Embedding Nikol'skiĭclasses into Lorentz spaces”, Siberian Math. J., 51:4 (2010), 728–744  mathnet  crossref  mathscinet  isi  elib  elib
    10. E. D. Kosov, “Klassy Besova na konechnomernykh i beskonechnomernykh prostranstvakh”, Matem. sb., 210:5 (2019), 41–71  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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