We study Hankel operators and CZ commutators in Lorentz and weak trace classes. It is known that for Hankel operators on Bergman space on the unit disk the two classes coincide.  We construct examples of CZ commutators on the torus which are in the weak trace ideal but not in the Lorentz ideal. We consider similar questions for Hankel operators on the Bergman and Hardy spaces on the unit ball. (Joint work with M. Goffeng, A. Usachev.)

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