Characterization of CMO via compactness of the commutators of bilinear fractional integral operators

2016/12/04 by Dinghuai Wang, Jiang Zhou, Wang, Dinghuai +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1612.01116

openalex publication_date 2016/12/04 · openalex created_date 2016/12/16 · openalex updated_date 2026/07/28

Abstract

Let I_α be the bilinear fractional integral operator, B_α be a more singular family of bilinear fractional integral operators and b=(b,b). Bényi et al. in \citeB1 showed that if b∈ \rm CMO, the \rm BMO-closure of C^∞_c(ℝⁿ), the commutator [b,B_α]_i(i=1,2) is a separately compact operator. In this paper, it is proved that b∈ \rm CMO is necessary for [b,B_α]_i(i=1,2) is a compact operator. Also, the authors characterize the compactness of the \bf iterated commutator [Πb,I_α] of bilinear fractional integral operator. More precisely, the commutator [Πb,I_α] is a compact operator if and only if b∈ \rm CMO.

Citations

• New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory

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