Journal of Operator Theory

Volume 95, Issue 1, Winter 2026 pp. 119-151.

Absolutely summing Carleson embeddings on weighted Fock spaces with $A_{\infty}$-type weights

Authors: Jiale Chen (1), Bo He (2), Maofa Wang (3)
Author institution: (1) School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China
(2) School of Mathematical Sciences, Fudan University, Shanghai 200433, China
(3) School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Summary: In this paper, we investigate the $r$-summing Carleson embeddings on weighted Fock spaces $F^p_{\alpha,w}$. By using duality arguments, translating techniques and block diagonal operator skills, we completely characterize the $r$-summability of the natural embeddings $I_d:F^p_{\alpha,w}\to L^p_{\alpha}(\mu)$ for any $r\geqslant 1$ and $p>1$, where $w$ is a weight on the complex plane $\mathbb{C}$ that satisfies an $A_p$-type condition. As applications, we establish some results on the $r$-summability of differentiation and integration operators, Volterra-type operators and composition operators. Especially, we completely characterize the boundedness of Volterra-type operators and composition operators on vector-valued Fock spaces for all $p\in (0,\infty)$, which were left open before for the case $p\in(1,2)$.

DOI: http://dx.doi.org/10.7900/jot.2024apr01.24
Keywords: $r$-summing operator, Carleson embedding, weighted Fock space, $A_p$-type weight

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