An example of a~completely continuous integral operator from $L_p$ to $L_p$ with positive kernel not belonging to $L_r$ $(r>1)$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 18 (1963) no. 4

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@article{RM_1963_18_4_a14,
     author = {D. V. Salekhov},
     title = {An example of a~completely continuous integral operator from $L_p$ to $L_p$ with positive kernel not belonging to $L_r$ $(r>1)$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1963},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/RM_1963_18_4_a14/}
}
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D. V. Salekhov. An example of a~completely continuous integral operator from $L_p$ to $L_p$ with positive kernel not belonging to $L_r$ $(r>1)$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 18 (1963) no. 4. http://geodesic.mathdoc.fr/item/RM_1963_18_4_a14/