Paraproducts and Hankel operators of Schatten class via \(p\)-John--Nirenberg theorem (Q705337)

The authors give a new proof (that does not use interpolation theorems) of the fact that a dyadic paraproduct is in the Schatten--von Neumann class \(S_p\) if and only if its symbol belongs to the Besov space \(B_p^d\). This allows the authors to give a new proof of the reviewer's description of the Hankel operators of class \(S_p\) for \(1<p<\infty\) [\textit{V.~V.\ Peller}, Integral Equations Oper. Theory 5, 244--272 (1982; Zbl 0478.47014)]. The same technique is used for little Hankel operators in several variables. Finally, the authors study products of dyadic paraproducts.