Moduli of continuity in 𝑅ⁿ and 𝐷⊂𝑅ⁿ

Ditzian, Z.

doi:10.1090/S0002-9947-1984-0732110-9

Moduli of continuity in $\textbf {R}^{n}$ and $D\subset \textbf {R}^{n}$
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Trans. Amer. Math. Soc. 282 (1984), 611-623 Request permission

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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