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  • 1 РОСТОВСКИЙ ИНЖЕНЕ РНО-СТРОИТЕЛЬНЫЙ ИНС ТИТУТ УЛ. СОЦИАЛИСТИЧЕСКА Я, 162 344 022 РОСТОВ-НА-ДОНУ СССР УЛ. СОЦИАЛИСТИЧЕСКА Я, 162 344 022 РОСТОВ-НА-ДОНУ СССР
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Letp=(p1,p2,...) be a vector with an infinite number of coordinates, 1≦pk≦,k=1,2,... On the set of random functions depending on infinite number of variables, a mixed norm ∥.p is introduced, and thus the spacesLp with mixed norm are defined. Part 1 contains observations of general properties of those spaces (in particular, convergence properties depending on the behaviour of the exponentspk ask→ ∞). Part 2 contains the proof of infinite-dimensional version of S. L. Sobolev's theorem (in mixed norm) for potentials of Wiener semigroup on infinite dimensional torusT.

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