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Mat. Zametki, 1976, Volume 19, Issue 2, Pages 187–200 (Mi mz7738)  

This article is cited in 6 scientific papers (total in 6 papers)

Certain embedding theorems

È. A. Storozhenko

Odessa State University

Abstract: We obtain necessary and sufficient conditions such that, for $f(x)$ from $L^p(0,1)$, the integral
$$ \int_0^1|f(x)|^q dx\quad(0<p<1,\quad p<q<p(1-p)^{-1}) $$
is convergent, or for $f\in L^p[0,1]$ for all $p\ge1$, the integral $\int_0^1e^{|f(x)|} dx$ is convergent.

Full text: PDF file (716 kB)

English version:
Mathematical Notes, 1976, 19:2, 113–120

Bibliographic databases:

UDC: 517
Received: 30.01.1974

Citation: È. A. Storozhenko, “Certain embedding theorems”, Mat. Zametki, 19:2 (1976), 187–200; Math. Notes, 19:2 (1976), 113–120

Citation in format AMSBIB
\Bibitem{Sto76}
\by \`E.~A.~Storozhenko
\paper Certain embedding theorems
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 2
\pages 187--200
\mathnet{http://mi.mathnet.ru/mz7738}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=410358}
\zmath{https://zbmath.org/?q=an:0349.41021|0339.41023}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 2
\pages 113--120
\crossref{https://doi.org/10.1007/BF01098742}


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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, V. G. Krotov, P. Oswald, “Direct and converse theorems of Jackson type in $L^p$ spaces, $0<p<1$”, Math. USSR-Sb., 27:3 (1975), 355–374  mathnet  crossref  mathscinet  zmath
    2. V. G. Krotov, “On differentiability of functions in $L^p$, $0<p<1$”, Math. USSR-Sb., 45:1 (1983), 101–119  mathnet  crossref  mathscinet  zmath
    3. V. I. Kolyada, “Estimates of rearrangements and imbedding theorems”, Math. USSR-Sb., 64:1 (1989), 1–21  mathnet  crossref  mathscinet  zmath
    4. V. I. Kolyada, “Rearrangements of functions and embedding theorems”, Russian Math. Surveys, 44:5 (1989), 73–117  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. M. M. Lekishvili, A. N. Danelia, “On deformation of certain functional classes in the spaces $C(T^m)$ and $L(T^m)$”, Sb. Math., 192:8 (2001), 1209–1224  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. 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
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