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I was reading the paper Norm Inequalities in Nonlinear Transforms (referenced in this question) but ran into difficulties, so I was wondering if anyone could help?

I think I follow the paper until I get to the main result/theorem, which begins:

"If $\sum_{n=0}^\infty |h_n(p)|^2 K(p,p)^{n} < \infty$ on $p \in E$ then ..."

My problem is that $h_n$ is never defined before, in, or immediately after the theorem. My best guess is that this is a typo and should read $d_n(p)$ (which makes perfect sense in context, at least afaict, in light of discussion in the paragraph after equation (1.9)), but I have a niggling doubt given the recurrence of the $h_n$ notation much later in the paper. Does my guess seem sensible, or have I missed something here?

Any thoughts much appreciated.

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It's certainly a typo. You can find the theorem in another source by the same author, where $h_n$ is $d_n$:

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