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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 \[ \left \| {\frac {{{\partial ^k}f\left ( x \right )}}{{\partial {\xi _1} \cdots \partial {\xi _k}}}} \right \| \leq {\sup _\xi }\left \| {\frac {{{\partial ^k}f\left ( x \right )}}{{\partial {\xi ^k}}}} \right \|\] 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.

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

  • Colin Bennett and Robert Sharpley, Interpolation of operators, Pure and Applied Mathematics, vol. 129, Academic Press, Inc., Boston, MA, 1988. MR 928802
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