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arXiv · 2510.01374

Bounded symbols of Toeplitz operators on Paley-Wiener spaces and a weak factorization theorem

Petr Kulikov
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Abstract

A classical result by R. Rochberg says that every bounded Toeplitz operator $T$ on the Hilbert Paley-Wiener space $\mathrm{PW}_a^2$ admits a bounded symbol $\varphi$. We generalize this result to Toeplitz operators on the Banach Paley-Wiener spaces $\mathrm{PW}_a^p$, $1 1$, $\frac{1}{p}+\frac{1}{q}=1$, any function $h$ belonging to $\mathrm{PW}^1_{2a}$ can be represented as $$h=\sum_{k\geqslant 0}f_k\bar{g}_k,\qquad f_k\in\mathrm{PW}_a^p,\,g_k\in\mathrm{PW}_a^q.$$

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Petr Kulikov. 2025-10-01. Bounded symbols of Toeplitz operators on Paley-Wiener spaces and a weak factorization theorem. https://arxiv.org/abs/2510.01374

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