Boundedness of composition operators induced by rational inner functions on weighted Bergman spaces of the bidisc equals transversal intersection of level sets for non-smooth symbols, assuming high-order tangential intersections at singularities.
On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type
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abstract
We study membership of rational inner functions on the bidisk $\mathbb{D}^2$ in a scale of Dirichlet spaces considered by Bera, Chavan, and Ghara, and in higher-order variants of these spaces. We give a characterization for membership in terms of the geometric concept of contact order of a rational inner function at its singular points, and we further record some consequences and variants of our main result.
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Composition operators and Rational Inner Functions on the bidisc: A geometric approach
Boundedness of composition operators induced by rational inner functions on weighted Bergman spaces of the bidisc equals transversal intersection of level sets for non-smooth symbols, assuming high-order tangential intersections at singularities.