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We provide a corrected proof of one of the two main results (Theorem 3.2) of the paper "The space of persistence diagrams on n points coarsely embeds into Hilbert space" [Proc. Amer. Math. Soc. 149 (2021), pp. 2693–2703]. [ABSTRACT FROM AUTHOR]

Using q-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 q-calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative. [ABSTRACT FROM AUTHOR]