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

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}. [ABSTRACT FROM AUTHOR]