Commutativity of Hankel and Toeplitz operators on the Hardy space of the n-torus

We consider Hankel and Toeplitz operators on H 2 ( T n ), the Hardy space of the n- torus T n . Given symbols phi and psi in L infinity ( T n ) with suitable properties, we obtain necessary and sufficient conditions for the Hankel operator H psi,n and the Toeplitz operator T phi,n to commute. We then extend the study to the more general situation where no assumptions are imposed on phi, and provide new, non-trivial necessary conditions for the commutativity of H psi,n and T phi,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. (c) 2024 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies.