TY - JOUR
T1 - Compactness of Riesz transform commutator associated with Bessel operators
AU - Duong, Xuan Thinh
AU - Li, Ji
AU - Mao, Suzhen
AU - Wu, Huoxiong
AU - Yang, Dongyong
PY - 2018/6/1
Y1 - 2018/6/1
N2 - Let λ > 0 and Δλ:=−d2dx2−2λxddx be the Bessel operator on R+:= (0,∞). We first introduce and obtain an equivalent characterization of CMO(R+, x2λdx). By this equivalent characterization and by establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function b ∈ BMO(R+, x2λdx) is in CMO(R+, x2λdx) if and only if the Riesz transform commutator xxxx is compact on Lp(R+, x2λdx) for all p ∈ (1,∞).
AB - Let λ > 0 and Δλ:=−d2dx2−2λxddx be the Bessel operator on R+:= (0,∞). We first introduce and obtain an equivalent characterization of CMO(R+, x2λdx). By this equivalent characterization and by establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function b ∈ BMO(R+, x2λdx) is in CMO(R+, x2λdx) if and only if the Riesz transform commutator xxxx is compact on Lp(R+, x2λdx) for all p ∈ (1,∞).
UR - http://www.scopus.com/inward/record.url?scp=85050149699&partnerID=8YFLogxK
UR - http://purl.org/au-research/grants/arc/DP140100649
UR - http://purl.org/au-research/grants/arc/DP160100153
U2 - 10.1007/s11854-018-0048-5
DO - 10.1007/s11854-018-0048-5
M3 - Article
AN - SCOPUS:85050149699
SN - 0021-7670
VL - 135
SP - 639
EP - 673
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 2
ER -