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Free interpolation of germs of analytic functions in Hardy spaces

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Abstract

One proves theorems on the interpolation of germs of analytic functions, defined in the neighborhoods of the interpolation nodes, in the Hardy spaces HP(0 < p ⩽ +∞), generalizing the corresponding results of N. K. Nikol'skii and V. I. Vasyunin for the classes H∞ and H2. One obtains estimates of the norms of the interpolating functions in terms of the parameter of the set on which the interpolation is performed.

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Authors
  1. S. A. Vinogradov
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  2. S. E. Rukshin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 107, pp. 36–45, 1982.

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Vinogradov, S.A., Rukshin, S.E. Free interpolation of germs of analytic functions in Hardy spaces. J Math Sci 36, 319–325 (1987). https://doi.org/10.1007/BF01839604

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  • DOI: https://doi.org/10.1007/BF01839604

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