Pick $0<q<1$ and consider the map from $\mathbb{R}^n$ to $\mathbb{R}^n$ that sends $x$ to $|x|^{q-1}x$. Is this map Hölder-continuous (I guess with exponent $\leq q$)? In dimension one, I can exploit the homogeneity of the inequality defined by Hölder-continuity; but how can I proceed in higher dimension?
2026-03-29 06:27:19.1774765639
Is this vector-valued map Hölder-continuous?
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