In this paper, we characterize the z-invariant subspaces that lie between the Bergman spaces Ap(G) and Ap(G\K), where 1 < p < ∞, G is a bounded region in C, and K is a closed subset of a simple, compact, C1 arc.
Copyright © 1994 London Mathematical Society.
The definitive version is available at: http://blms.oxfordjournals.org/content/26/5/472.full.pdf+html
Ross, William T. "Invariant Subspaces of Bergman Spaces on Slit Domains." Bulletin of the London Mathematical Society 26, no. 5 (1994): 472-482. doi:10.1112/blms/26.5.472.
Ross, William T., "Invariant Subspaces of Bergman Spaces on Slit Domains" (1994). Math and Computer Science Faculty Publications. 36.