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

Jiale Chen; Bo He; Maofa Wang

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arXiv · 2505.16109

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

Jiale Chen·Bo He·Maofa Wang

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Abstract

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 $r\geq1$ 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 $1<p<\infty$, which were left open before for the case $1<p<2$.

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BibTeX RIS

Jiale Chen, Bo He, Maofa Wang. 2025-05-22. Absolutely summing Carleson embeddings on weighted Fock spaces with $A_{\infty}$-type weights. https://arxiv.org/abs/2505.16109

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