A Sharp Capacity Gauge Solution to the Open Problem of Quasisymmetric Composition on ${\mathcal{Q}}_{\alpha }({\mathbb{R}}^n)$

Liu Liguang, Xiao Jie

The spaces ${\mathcal{Q}}_{\alpha }({\mathbb{R}}^n)$ for the critical index range $\alpha \in (0,\min \{1,n/2\})$ form a scale-invariant family lying strictly between the space of constant functions and…