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

We give an interpolation-free proof of the known fact that a dyadic paraproduct is of Schatten–von Neumann class Sp, if and only if its symbol is in the dyadic Besov space Bpd. 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 Pellerʹs characterizations of scalar and vector Hankel operators of Schatten–von Neumann class Sp for 1