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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
DOI: https://doi.org/10.1090/S0002-9939-1990-0994773-0
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.

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