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Proceedings of the American Mathematical Society

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Mixed and directional derivatives


Authors: W. Chen and Z. Ditzian
Journal: Proc. Amer. Math. Soc. 108 (1990), 177-185
MSC: Primary 26D10; Secondary 41A44
MathSciNet review: 994773
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Abstract: The estimate

$\displaystyle \left\Vert {\frac{{{\partial ^k}f\left( x \right)}}{{\partial {\x... ...Vert {\frac{{{\partial ^k}f\left( x \right)}}{{\partial {\xi ^k}}}} \right\Vert$

is proved for various spaces of functions over domains in $ {R^d}$ , where $ \partial f / \partial {\xi _i}$ is the directional derivative of $ f$ in the $ {\xi _i}$, direction and $ {\xi _1}, \ldots ,{\xi _k}$ are any $ k$ directions.

References [Enhancements On Off] (What's this?)

  • [1] Colin Bennett and Robert Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol. 129, Academic Press, Inc., Boston, MA, 1988. MR 928802
  • [2] Z. Ditzian, Multivariate Landau-Kolmogorov-type inequality, Math. Proc. Cambridge Philos. Soc. 105 (1989), no. 2, 335–350. MR 974990, 10.1017/S0305004100067839
  • [3] Robert C. Sharpley, Cone conditions and the modulus of continuity, Second Edmonton conference on approximation theory (Edmonton, Alta., 1982), CMS Conf. Proc., vol. 3, Amer. Math. Soc., Providence, RI, 1983, pp. 341–351. MR 729339
  • [4] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095

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DOI: https://doi.org/10.1090/S0002-9939-1990-0994773-0
Article copyright: © Copyright 1990 American Mathematical Society