Schatten class estimates for paraproducts in multiparameter setting

Abstract

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