Necessary and sufficient conditions for boundedness of commutators of bilinear Hardy-Littlewood maximal function

2017/08/31 by Wang, Dinghuai, Zhou, Jiang
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1708.09549

Abstract

Let M be the bilinear Hardy-Littlewood maximal function and b=(b,b) be a collection of locally integrable functions. In this paper, the authors establish characterizations of the weighted \rm BMO space in terms of several different commutators of bilinear Hardy-Littlewood maximal function, respectively; these commutators include the maximal iterated commutator M_Πb, the maximal linear commutator M_Σb, the iterated commutator [Πb,M] and the linear commutator [Σb,M].

Related

• Boundedness and Compactness of commutator of Hardy-Littlewood maximal operator
• Commutators of the maximal and sharp functions with weighted Lipschitz functions
• Commutators of Maximal Operators on Weighted Morrey Spaces
• New Multilinear Littlewood--Paley g_λ^* Function and Commutator on weighted Lebesgue Spaces
• Necessary conditions for the boundedness of linear and bilinear commutators on Banach function spaces