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Schatten classes and commutators in the two weight setting, II. Riesz transforms

Schatten classes and commutators in the two weight setting, II. Riesz transforms

We characterize the Schatten class $S^p$ of the commutator of Riesz transforms $[b,R_j]$ in $\mathbb R^n$ ($j=1,\ldots, n$) in the two weight setting for $n< p<\infty$, by introducing the condition that the symbol $b$ being in Besov spaces associated with the given two weights. At the critical index $p=n$, the …