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

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Matematicheskie Zametki, 1976, Volume 19, Issue 2, Pages 187–200 (Mi mzm7738)

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

Certain embedding theorems

È. A. Storozhenko

Odessa State University

Full-text PDF (716 kB) Citations (6)

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.

Received: 30.01.1974

English version:
Mathematical Notes, 1976, Volume 19, Issue 2, Pages 113–120
DOI: https://doi.org/10.1007/BF01098742

Bibliographic databases:

UDC: 517

Language: Russian

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/mzm7738}

\mathscinet{http://mathscinet.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}

Linking options:

https://www.mathnet.ru/eng/mzm7738

https://www.mathnet.ru/eng/mzm/v19/i2/p187

This publication is cited in the following 6 articles:

V. A. Andrienko, “Embedding of $H_p^\omega$ in the class $e^L$ ”, Russian Math. (Iz. VUZ), 54:3 (2010), 1–6
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
V. I. Kolyada, “Rearrangements of functions and embedding theorems”, Russian Math. Surveys, 44:5 (1989), 73–117
V. I. Kolyada, “Estimates of rearrangements and imbedding theorems”, Math. USSR-Sb., 64:1 (1989), 1–21
V. G. Krotov, “On differentiability of functions in $L^p$ , $0<p<1$ ”, Math. USSR-Sb., 45:1 (1983), 101–119
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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