Paraproducts and Hankel operators of Schatten class via p-John-Nirenberg Theorem

摘要

We give an interpolation-free proof of the known fact that a dyadic paraproduct is of Schatten-von Neumann class S-p if and only if its symbol is in the dyadic Besov space B-p(d). our main tools are a product formula for paraproducts and a "p-John-Nirenberg-Theorem" due to Rochberg and Semmes.We use the same technique to prove a corresponding result for dyadic paraproducts with operator symbols.Using an averaging technique by Petermichl, we retrieve Peller's characterizations of scalar and vector Hankel operators of Schatten-von Neumann class S-p for 1