Rational inner functions with one boundary singularity are claimed to induce unbounded composition operators on the bidisc Bergman space, while stable polynomial symbols give bounded operators between weighted Bergman spaces.
Knese, Inner functions on the bidisk and associated Hilbert spaces , Journal of Functional Analysis Volume 265, Issue 11 , 1 December 2013, Pages 2753-2790
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Composition operators and Rational Inner Functions on the bidisc
Rational inner functions with one boundary singularity are claimed to induce unbounded composition operators on the bidisc Bergman space, while stable polynomial symbols give bounded operators between weighted Bergman spaces.