arXiv subjects

Ermin Wang

Publications and source records attributed to Ermin Wang.

2 recordsLinked to original sources

arXiv2025

Absolutely Summing Toeplitz operators on Bergman spaces in the unit ball of $\mathbb{C}^n$

In this paper, for $p> 1 $ and $r \ge 1$ we provide a complete characterization of the positive Borel measures $\mu$ on the unit ball $\B_n$ of $\mathbb {C}^n$ for which the induced Toeplitz operator $T_\mu$ is $r$-summing on the Bergman space $A^{p}$. We prove that the $r$-summing norm of $T_\mu: A^p\to A^p$ is equivalent to $\|\widetilde{\mu}\|_{L^{\kappa}(d\lambda)}$, where $\kappa$ is a positive number determined by $p$ and $r$. As some preliminary, we describe when a Carleson embedding $J_\mu: A^p \to L^q(\mu) (1\le p, q\le 2)$ is $r$-summing, which extends the main result in [B. He, et al, Absolutely summing Carleson embeddings on Bergman spaces, Adv. Math., 439, 109495 (2024)].

math.FA↗

arXiv2025

Absolutely Summing Toeplitz operators on Fock spaces

For $1\le p<\infty$, let $F^p_\varphi$ be the Fock spaces on ${\mathbb C}^n$ with the weight function $\varphi$ that $\varphi \in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right)$ is real-valued and satisfies $ m{\omega }_{0} \leq d{d}^{c}\varphi \leq M{\omega }_{0} $ for two positive constants $m$ and $M$, ${\omega }_{0} = d{d}^{c}{\left| z\right| }^{2}$ is the Euclidean K\"{a}hler form on ${\mathbb{C}}^{n}$, ${d}^{c} = \frac{\sqrt{-1}}{4}\left( {\bar{\partial } - \partial }\right)$. In this paper, we completely characterize those positive Borel measure $\mu$ on ${\mathbb C}^n$ so that the induced Toeplitz operators $T_\mu$ is $r$-summing on $F_{\varphi}^{p}$ for $r \ge 1$.

math.FA↗