We prove that a function in several variables is the local Zygmund class $\mathcal{Z}^{m,1}$ if and only its composite with every smooth curve of $\mathcal{Z}^{m,1}$. This complements well-known analogous result for Hölder–Lipschitz classes $\mathcal{C}^{m,\alpha}$, which we reprove along way. demonstrate these results generalize to mappings between Banach spaces use them study regularity super...
