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Conjugate of the Sobolev space of vector-valued functions

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Abstract

Necessary and sufficient conditions are derived for the equality WℓE(X)*=WℓE'(X*), where E is a symmetric space, X a Banach space, ℓ > 0 is an integer.

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Literature cited

  1. A. V. Bukhvalov, “Continuity of operators in spaces of measurable vector functions with applications to the study of Sobolev spaces and analytical functions in the vector-valued case,” Dokl. AN SSSR,246, No. 3, 524–528 (1979).

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  2. T. McConnell, “On Fourier multiplier transformations of Banach-valued functions,” Trans. AMS,285, No. 2, 739–757 (1984).

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Authors
  1. A. V. Bukhvalov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 159, pp. 119–120, 1987.

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Bukhvalov, A.V. Conjugate of the Sobolev space of vector-valued functions. J Math Sci 47, 2908–2909 (1989). https://doi.org/10.1007/BF01305220

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  • DOI: https://doi.org/10.1007/BF01305220

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