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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Moduli of continuity in $ {\bf R}\sp{n}$ and $ D\subset {\bf R}\sp{n}$

Author: Z. Ditzian
Journal: Trans. Amer. Math. Soc. 282 (1984), 611-623
MSC: Primary 26B05; Secondary 41A25, 46E35
MathSciNet review: 732110
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Abstract: The $ r$ modulus of continuity for $ f \in C({R^n})$ is expressed in terms of $ r$ moduli of continuity in $ n$ independent directions. Generalizations to other spaces of functions on $ {R^n}$ or $ D \subset {R^n}$ are also given.

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Additional Information

PII: S 0002-9947(1984)0732110-9
Keywords: Moduli of continuity in $ {R^n}$ smoothness of function spaces, multivariate semigroups of contractions
Article copyright: © Copyright 1984 American Mathematical Society