四元数Hardy空间的Corona定理
Corona theorem for the quaternionic Hardy space
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中文总结 AI 辅助
该研究针对四元数Hardy空间，将有界切片正则函数的有限生成元Corona定理推广至可数多个生成元，同时建立对应的Toeplitz Corona定理，解决了相关文献提出的问题。
中文摘要 AI 辅助
F. Colombo、E. Pozzi、I. Sabadini和B. D. Wick近期在《Int. Math. Res. Not. IMRN》2026年第11期（论文编号rnag107）中建立了四元数单位球上有界切片正则函数的有限生成元Corona定理。我们证明了可数多个有界切片正则生成元的Corona定理及Toeplitz Corona定理，从而回答了该论文提出的两个问题。我们的结果将有限生成元Corona定理推广到可数多个生成元的情形，并在四元数Hardy空间上建立了其Hilbert空间对应形式。
英文摘要
The finite-generator corona theorem for bounded slice regular functions on the quaternionic unit ball was recently established by Colombo, Pozzi, Sabadini, and Wick. In the present paper, we extend the quaternionic \(H^\infty\)-corona theorem to countably many generators and obtain quantitative estimates that are independent of the cardinality of the generating family. We also establish the corresponding \(H^p\)-corona theorem for the full range \(1\leq p<\infty\), with quantitative norm estimates for both finite and countable families of generators. In the Hilbert-space setting, we prove a quaternionic Leech factorization theorem for Hardy-space multipliers and derive, as a consequence, a Toeplitz corona characterization. Our approach is based on a fixed-slice \(2\times2\) complex matrix realization of the slice regular product, together with operator-valued corona and factorization techniques.
