On the weak boundedness of multilinear Littlewood--Paley functions

In this note, notwithstanding the generalization, we simplify and shorten the proofs of the main results of the third author's paper \cite{SXY} significantly. In particular, the new proof for \cite[Theorem 1.1]{SXY} is quite short and, unlike the original proof, does not rely on the properties of the "Marcinkiewicz function". This... Show more