Fredholm composition operators on Hardy-Sobolev spaces with bounded reproducing kernel

He, Li

doi:10.1090/proc/16319

Fredholm composition operators on Hardy-Sobolev spaces with bounded reproducing kernel
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by Li He;

Proc. Amer. Math. Soc. 151 (2023), 3457-3468

DOI: https://doi.org/10.1090/proc/16319

Published electronically: May 12, 2023

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Abstract:

For any real $\beta$ let $H^2_\beta$ be the Hardy-Sobolev space on the unit ball $\mathbb {B}_{n} , n\geq 1$. $H^2_\beta$ is a reproducing kernel Hilbert space and its reproducing kernel is bounded when $\beta >n/2$. In this paper, we characterize when the composition operator $C_{\varphi }$ on $H^{2}_{\beta }$ is Fredholm for a non-constant analytic map $\varphi :\mathbb {B}_{n}\to \mathbb {B}_{n}$ .

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