Commutators of Littlewood-Paley operators (Q1047877)

The authors prove an extension of \textit{A. Uchiyama}'s famous result [Tohoku Math. J., II. Ser. 30, 163--171 (1978; Zbl 0384.47023)]. They discuss the \(L^p\) boundedness of commutators \([b,L]\), where \(b\in BMO(\mathbb{R}^n)\) and \(L\) denote the Littlewood-Paley operators including the Littlewood-Paley \(g\) function, Lusin area integral and \(g_\lambda^*\) function. The setting conditions of \(L\) are weaker than the traditional setting, thus the results are meaningful and nontrivial.