Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Mixed and directional derivatives
HTML articles powered by AMS MathViewer

by W. Chen and Z. Ditzian PDF
Proc. Amer. Math. Soc. 108 (1990), 177-185 Request permission


The estimate \[ \left \| {\frac {{{\partial ^k}f\left ( x \right )}}{{\partial {\xi _1} \cdots \partial {\xi _k}}}} \right \| \leq {\sup _\xi }\left \| {\frac {{{\partial ^k}f\left ( x \right )}}{{\partial {\xi ^k}}}} \right \|\] 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.
  • Colin Bennett and Robert Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol. 129, Academic Press, Inc., Boston, MA, 1988. MR 928802
  • Z. Ditzian, Multivariate Landau-Kolmogorov-type inequality, Math. Proc. Cambridge Philos. Soc. 105 (1989), no. 2, 335–350. MR 974990, DOI 10.1017/S0305004100067839
  • 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
  • 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
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 177-185
  • MSC: Primary 26D10; Secondary 41A44
  • DOI:
  • MathSciNet review: 994773