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Some imbedding theorems for the function spaces − fr,ρ,θ λ,ϕ,bs (G)

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Abstract

One considers imbedding type theorems for the spaces − fr,ρ,θ λ,ϕ,bs (G) of real functions, defined on a domain G of then -dimensional Euclidean space En. As opposed to the known spaces of this type, the power function ta, characterizing the degree of the smoothness of the functions, is replaced here by a function ϕ(t), arbitrary in a certain sense.

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 70, pp. 49–75, 1977.

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Il'in, V.P. Some imbedding theorems for the function spaces − fr,ρ,θ λ,ϕ,bs (G). J Math Sci 23, 1909–1929 (1983). https://doi.org/10.1007/BF01093274

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Keywords

  • Euclidean Space
  • Function Space
  • Power Function
  • Real Function
  • Type Theorem