Author

Jie Xiao

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Preprint Jul 2026

On the holomorphic differential operator $\frac{d}{dz}: Q_K\to L^q(WdA)$

In this paper, we obtain non-testing characterizations, in terms of dyadic capacity gauges, of the boundedness and compactness of the differentiation operator $$ \frac{d}{dz}:Q_K\longrightarrow L^q(W\,dA), \qquad 0<q<\infty. $$ We also characterize the limiting case as $q\to0^+$, formulated in terms of a logarithmic ge...

Bing-Yang Hu, S. Luo, Jie Xiao et al. · 0 citations

Preprint Jul 2026

On the growth of Bloch functions

We prove that there exist two Bloch functions $f_1$ and $f_2$ on $\mathbb D$ such that $$ |f_1(z)|+|f_2(z)| \geq \left(\log\frac{1}{1-|z|}\right)^{1/2}, \qquad z\in\mathbb D, $$ thereby resolving an open problem posed in 2008 by Girela, Pel\'aez, P\'erez-Gonz\'alez and R\"atty\"a. Our proof is based on a new Szeg\H{o}-...

Bing-Yang Hu, Jie Xiao, Xiao-Jing Zhou · 0 citations