Geodesic
Multilinear and power functionals and operators in the space of continuous functions
Trudy Instituta matematiki, Tome 20 (2012) no. 2, pp. 18-29

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The article deals with multilinear and power integral operators in the space of continuous functions. It is described necessary and sufficient conditions on kernels of integral operators that guarantee the action of these operators in the space of continuous functions, their weak compactness and compactness. It is also shown that the space of these operators with the natural norm is not complete. 
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     author = {P. P. Zabreǐko},
     title = {Multilinear and power functionals and operators in the space of continuous functions},
     journal = {Trudy Instituta matematiki},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2012_20_2_a2/}
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P. P. Zabreǐko. Multilinear and power functionals and operators in the space of continuous functions. Trudy Instituta matematiki, Tome 20 (2012) no. 2, pp. 18-29. http://geodesic.mathdoc.fr/item/TIMB_2012_20_2_a2/