Characterizations of VMO and CMO Spaces in the Bessel Setting  

作　　者：Qing Dong GUO Jorge J.BETANCOR Dong Yong YANG 

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen,361005,P.R.China [2]Departamento de Anáisis Matemáico,Universidad de La Laguna,Campus de Anchieta,Avda.Astrofísico Francisco Sánchez,s/n,38271,La Laguna(Sta.Cruz de Tenerife),Spain

出　　处：《Acta Mathematica Sinica,English Series》2024年第12期3055-3078,共24页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11971402 and 12171399);Spanish Government(Grant No.PID2019-106093GB-I00)。

摘　　要：Letλ>0 and △λ:=-dx^(2)/d^(2)-x/2λdx/d be the Bessel operator on ℝ+:=(0,∞).In this paper,the authors introduce and characterize the space VMO(ℝ+,dmλ)in terms of the Hankel translation,the Hankel convolution and a John-Nirenberg inequality,and obtain a sufficient condition of Fefferman-Stein type for functions f∈VMO(ℝ+,dmλ)using R△λ,the adjoint of the Riesz transform R△λ.Furthermore,we obtain the characterization of CMO(ℝ+,dmλ)in terms of the John-Nirenberg inequality which is new even for the classical CMO(ℝ^(n))and a sufficient condition of Fefferman-Stein type for functions f∈CMO(ℝ+,dmλ).

关 键 词：Bessel operator VMO(ℝ+ dmλ) CMO(ℝ+ dmλ) Riesz transform 

分 类 号：O177[理学—数学]