Compactness of Riesz transform commutator associated with Bessel operators

2016/04/09 by Duong, Xuan Thinh, Li, Ji, Mao, Suzhen +2 · 1 citation
#42B20 #42B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.02503

Abstract

Let λ>0 and \triangle_λ:=-(d²)/(dx²)-(2λ)/(x) \frac ddx be the Bessel operator on \mathbb R₊:=(0,∞). We first introduce and obtain an equivalent characterization of \rm CMO(\mathbb R₊, x^2λdx). By this equivalent characterization and establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function b∈ \rm BMO(\mathbb R₊, x^2λdx) is in \rm CMO(\mathbb R₊, x^2λdx) if and only if the Riesz transform commutator [b, R_Δλ] is compact on L^p(\mathbb R₊, x^2λdx) for any p∈(1, ∞).

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