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Mat. Sb. (N.S.), 1985, Volume 127(169), Number 3(7), Pages 352–383 (Mi msb2001)  

This article is cited in 3 scientific papers (total in 3 papers)

On embedding $H_p^{\omega_1,…,\omega_\nu}$ classes

V. I. Kolyada


Abstract: Necessary and sufficient conditions are obtained for embedding the function classes $H_p^{\omega_1,…,\omega_\nu}$, with given majorants of partial $L_p$-moduli of continuity, in the space $L_q([0,1]^\nu)$ ($1\leqslant p<q<\infty$). In particular, for Lipschitz classes $H_p^{\delta^{\alpha_1},…,\delta^{\alpha_\nu}}$ ($0<\alpha_i\leqslant1$) a criterion is obtained for embedding in $L_q$ with limit exponent $q=\frac p{1-\overline\alpha p}$, where $\overline\alpha=(\frac1{\alpha_1}+…+\frac1{\alpha_\nu})^{-1}$.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Sbornik, 1986, 55:2, 351–381

Bibliographic databases:

UDC: 517.5
MSC: Primary 46E35; Secondary 26B35
Received: 27.02.1984

Citation: V. I. Kolyada, “On embedding $H_p^{\omega_1,…,\omega_\nu}$ classes”, Mat. Sb. (N.S.), 127(169):3(7) (1985), 352–383; Math. USSR-Sb., 55:2 (1986), 351–381

Citation in format AMSBIB
\Bibitem{Kol85}
\by V.~I.~Kolyada
\paper On~embedding $H_p^{\omega_1,\dots,\omega_\nu}$ classes
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 127(169)
\issue 3(7)
\pages 352--383
\mathnet{http://mi.mathnet.ru/msb2001}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=798382}
\zmath{https://zbmath.org/?q=an:0605.41034}
\transl
\jour Math. USSR-Sb.
\yr 1986
\vol 55
\issue 2
\pages 351--381
\crossref{https://doi.org/10.1070/SM1986v055n02ABEH003009}


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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, “Estimates of rearrangements and imbedding theorems”, Math. USSR-Sb., 64:1 (1989), 1–21  mathnet  crossref  mathscinet  zmath
    2. V. I. Kolyada, “Rearrangements of functions and embedding theorems”, Russian Math. Surveys, 44:5 (1989), 73–117  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Perez, FJ, “Embedding theorems for anisotropic Lipschitz spaces”, Studia Mathematica, 168:1 (2005), 51  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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