Schatten class estimates for paraproducts in multiparameter setting

Source abstract

Let $\Pi_{b}$ be a bounded $n$ parameter paraproduct with symbol $b$. We demonstrate that this operator is in the Schatten class $\mathbb{S}^{p}$, $0 < p < \infty$, if the symbol is in the $n$ parameter Besov space $\mathbb{B}^{p}$. Our result covers both the dyadic and continuous version of the paraproducts in the multiparameter setting.