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Using π‘ž-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their π‘ž-calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative.


This is a pre-copy-editing, author-produced PDF of an article that later underwent peer review and was accepted for publication in Proceedings of the American Mathematical Society in 2024. This article may not exactly replicate the final published version. The definitive publisher-authenticated version is available online at

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American Mathematical Society



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