arXiv subjects
Publications and source records attributed to Liangying Jiang.
In this article, we investigate the (big) Hankel operators $H_f$ on Hardy spaces of strongly pseudoconvex domains with smooth boundaries in $\mathbb{C}^n$. We also give a necessary and sufficient condition for boundedness of the Hankel operator $H_f$ on the Hardy space of the unit disc, which is new in the setting of one variable.
We study composition operators on the Fock spaces $\mathcal{F}^2_α(\mathbb{C}^n)$, problems considered include the essential norm, normality, spectra, cyclicity and membership in the Schatten classes. We give perfect answers for these basic properties, which present lots of different characterizations with the composition operators on the Hardy space or the weighted Bergman spaces.
In this paper, we investigate the compactness of the commutator $[C_ψ^{\ast}, C_φ]$ on the Hardy space $H^2(B_N)$ or the weighted Bergman space $A^2_s(B_N)$ ($s>-1$), when $φ$ and $ψ$ are automorphisms of the unit ball $B_N$. We obtain that $[C_ψ^{\ast}, C_φ]$ is compact if and only if $φ$ and $ψ$ commute and they are both unitary. This generalizes the corresponding result in one variable. Moreover, our technique is different and simpler. In addition, we also discuss the commutator $[C_ψ^{\ast}, C_φ]$ on the Dirichlet space $\mathcal{D}(B_N)$, where $φ$ and $ψ$ are linear fractional self-maps or both automorphisms of $B_N$.
We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>-1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we investigate the automorphic composition operators on the Hardy space $H^2(B_N)$ and the weighted Bergman spaces $A^2_s(B_N)$ ($s>-1$). Furthermore, we give some composition operators induced by linear fractional self-maps of the unit ball $B_N$ that are not essentially normal.
We characterize the spectra of composition operators on the Hardy space $H^2(B_N)$, when the symbols are elliptic or hyperbolic linear fractional self-maps of $B_N$. Therefore, combining with the result obtained by Bayart \cite{B10}, the spectra of all linear fractional composition operators on $H^2(B_N)$ are completely determined.
We find a lower bound for the essential norm of the difference of two composition operators acting on $H^2(B_N)$ or $A^2_s(B_N)$ ($s>-1$). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.