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Hankel Operators on Bounded Analytic Functions

For U a domain in the complex plane and g a bounded measurable function on U , the generalized Hankel operator Sg on H∞(U) is the operator of multiplication by g followed by projection into L∞/H∞. Under certain conditions on U we show that either Sg is compact or there is an embedded `∞ on which Sg is bicontinuous. We characterize those g’s for which Sg is compact in the case that U is a Behrens roadrunner domain.