Geodesic
Certain embedding theorems
Matematičeskie zametki, Tome 19 (1976) no. 2, pp. 187-200 
È. A. Storozhenko. Certain embedding theorems. Matematičeskie zametki, Tome 19 (1976) no. 2, pp. 187-200. http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a3/
@article{MZM_1976_19_2_a3,
     author = {\`E. A. Storozhenko},
     title = {Certain embedding theorems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {187--200},
     year = {1976},
     volume = {19},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a3/}
}
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JO  - Matematičeskie zametki
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IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_1976_19_2_a3/
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ID  - MZM_1976_19_2_a3
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.