Commutators of Littlewood-Paley operators on the generalized Morrey space (Q1957639)

Let \(T\) be one of the following: the Marcinkiewicz integral, the parameterized area integral or the parameterized Littlewood-Paley \(g_\lambda^\ast\)-function. The authors show that if the commutator \([b,T]\) is bounded in a generalized Morrey space \(L^{p,\varphi}(\mathbb{R}^n)\), under some assumptions on this space, then \(b\) is necessarily in \(BMO\).