Commutators [b,T] are in S^p on (quasi-)metric spaces iff b is in a Besov space for p>d, constant for p≤d, and in a Sobolev space for the weak class at p=d.
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Schatten properties of commutators on metric spaces
Commutators [b,T] are in S^p on (quasi-)metric spaces iff b is in a Besov space for p>d, constant for p≤d, and in a Sobolev space for the weak class at p=d.