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Growth of a mixed derivative of a function of\(C^{(l_1 , l_2 )}\)

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Abstract

For a function f(x, y) with the continuous derivatives\(D_1^{l_1 } f,{\text{ }}D_2^{l_2 } f\) we estimate the growth of the mixed derivative Dα f(α1/l 1+α2/l 2=1). We consider generalizations and related problems.

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Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR

    O. V. Besov

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  1. O. V. Besov
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Translated from Matematicheskie Zametki, Vol. 15, No. 3, pp. 355–362, March, 1974.

In conclusion, the author wishes to thank K. I. Oskolkov for pointing out to him concepts for the discussion of the statement of the problem.

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Besov, O.V. Growth of a mixed derivative of a function of\(C^{(l_1 , l_2 )}\) . Mathematical Notes of the Academy of Sciences of the USSR 15, 201–206 (1974). https://doi.org/10.1007/BF01438370

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  • DOI: https://doi.org/10.1007/BF01438370

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