Year: 2026
Type: preprint
Abstract: Let \(η=(η_n)_{n\ge0}\) be a complex sequence such that \(F_η(z)=\sum_{n\ge0}η_nz^n\in\Hol(\D)\), and let \(\mathcal R_{(η)}\) be the associated Rhaly operator. We give a complete characterization of boundedness and compactness of \(\mathcal R_{(η)}:\mathcal D^p_α\to\mathcal D^q_β\) for \(1-1\). The characterization is formulated in terms of the \(H^q\)-norms of the dyadic blocks of \(F_η\). For \(-1<αp-2\), boundedness is characterized by membership in analytic truncated Besov spaces and analytic Besov spaces, respectively; compactness has the same characterization for \(q2\), we also construct a symbol \(F_η\in H^\infty\capλ^p_{1/p}\) for which \(\mathcal R_{(η)}\) is not bounded on \(H^p\).
Source: arXiv (Cornell University)
Author: Shi, Yecheng
Institution: Lingnan Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213350206