Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26D10, 41A44

Retrieve articles in all journals with MSC: 26D10, 41A44

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society