Abstract
We consider Hankel and Toeplitz operators on H2(Tn), the Hardy space of the n-torus Tn. Given symbols φ and ψ in L∞(Tn) with suitable properties, we obtain necessary and sufficient conditions for the Hankel operator Hψ,n and the Toeplitz operator Tφ,n to commute. We then extend the study to the more general situation where no assumptions are imposed on φ, and provide new, non-trivial necessary conditions for the commutativity of Hψ,n and Tφ,n. We also show that certain well known commutativity results between Hankel and Toeplitz operators in the one-variable case do not extend to the multivariable setting.
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