Author

Tai-Liang Liu

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Preprint Aug 2026

A Compactness Characterization of Strongly Symmetric Homeomorphisms

A self-homeomorphism $h$ of the unit circle $\mathbb{T}$ is strongly symmetric if it is absolutely continuous and $\log h'\in\text{VMO}(\mathbb{T})$. Let $P_h^-$ be the anti-analytic component of the pullback operator $P_h: F\mapsto F\circ h$ on $\text{BMOA}(\mathbb{D})$, where $\mathbb{D}$ is the unit disk. P. Jones p...

Tai-Liang Liu, Yu-Liang Shen · 1 citation

Preprint Sep 2026

Real-analytic realization of universal Teichm\"uller space via complex-structures on $H^{1/2}$

Let $H$ be the Hilbert transform, let $h$ be a quasisymmetric homeomorphism of the unit circle $S^1$, and set $V_hu=u\circ h$ and $J_h=V_hHV_h^{-1}$, defined on the Sobolev space $H^{1/2}(S^1)$. We prove that $h\mapsto V_h$ is nowhere continuous in operator norm, although it is continuous in the strong operator topolog...

Tai-Liang Liu, Yu-Liang Shen · 0 citations