Oscillation and variation for Riesz transform in setting of Bessel operators on H1 and BMO  

作　　者：Xiaona CUI Jing ZHANG 

机构地区：[1]College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China [2]School of Mathematics and Statistics,Yili Normal University,Yining 835000,China

出　　处：《Frontiers of Mathematics in China》2020年第4期617-647,共31页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported in part by the Doctoral Scientific Research of Yili Normal University(No.2017YSBS09).

摘　　要：Letλ〉0,and let the Bessel operator△λ:=-d2/dx2-2λ/x d/dx defined on R+:=(0,∞).We show that the oscillation andρ-variation operators of the Riesz transform R△λassociated with△λare bounded on BMO(R+,dmλ),whereρ>2 and dmλ=x2λdx.Moreover,we construct a(1,∞)△λ-atom as a counterexample to show that the oscillation andρ-variation operators of R△λare not bounded from to L1(R+,dmλ).Finally,we prove that the oscillation and theρ-variation operators for the smooth truncations associated with Bessel operators R~△λare bounded from H1(R+:dmλ)to L1(R+,dmλ).

关 键 词：Oscillation operator variation operator Bessel operator 

分 类 号：O17[理学—数学]