Abstract:In this paper, we obtain a complete classification of Toeplitz + Hankel operators on the vector-valued Hardy space $H^2_{\mathcal{E}}(\mathbb{D}^n)$ over the polydisc $\mathbb{D}^n$ in $\mathbb{C}^n$ for $n\geq 1$. We also characterize the paired operators on $L^2(\mathbb{T}^n)$. For an inner function $\theta \in H^\infty(\mathbb{D}^n)$, we further characterize $\theta$-paired operators on $H^2(\mathbb{D}^n)$ with respect to the Beurling submodule $\theta H^2(\mathbb{D}^n)$.
From: Amit Maji [view email]
[v1]
Sun, 21 Jun 2026 20:15:24 UTC (11 KB)
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