Journal of Operator Theory

Volume 94, Issue 2, Autumn 2025 pp. 513-526.

Toeplitz operators on the $n$-dimensional Hartogs triangle

Authors: Shubham Jain (1), Paramita Pramanick (2)
Author institution: (1) Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India
(2) Statistics and Mathematics unit, Indian Statistical Institute Kolkata, Kolkata 700108, India

Summary: We formally introduce and study Toeplitz operators on the Hardy space of the $n$-dimensional Hartogs triangle. We find a precise relation between these operators and the Toeplitz operators on the Hardy space of the unit polydisc $\mathbb D^n.$ As an application, we deduce several properties of these operators from their polydisc counterparts. Furthermore, we show that certain results achieved for the Toeplitz operators on the $n$-dimensional Hartogs triangle are not the same as those in the polydisc case.

DOI: http://dx.doi.org/10.7900/jot.2024feb14.2456
Keywords: Toeplitz operators, Hardy spaces, Hartogs triangle

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