Abstract
The function class W 1f (G, A) is defined. A general problem concerning necessary and sufficient conditions under which this class can be imbedded in the space C(G) of functions continuous on G is posed, and the special case of this problem in which the function f(x1, x2,..., xn) involved in the definition of w 1f (G, A) on\(\left| X \right| = \sqrt {X_1^2 + X_2^2 + ... + X_n^2 } \) is solved.
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A. D. Ioffe and V. M. Tikhomirov, “Duality of convex functions and extremal problems,” Uspekhi Matem. Nauk,23, 6, 51–116 (1968).
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Translated from Matematicheskie Zametki, Vol. 9, No. 6, pp. 639–650, June, 1971.
In conclusion, the author wishes to thank V. M. Tikhomirov for posing the problem and for his criticism and advice. Thanks are also due to S. B. Stechkin for his interest in the work.
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Rozenfel'd, E.A. Conditions for the imbedding of the function class W 1f (G, A) in the space C(G). Mathematical Notes of the Academy of Sciences of the USSR 9, 371–377 (1971). https://doi.org/10.1007/BF01094578
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DOI: https://doi.org/10.1007/BF01094578