Θ-type Calderón-Zygmund Operators with Non-doubling Measures  

作　　者：Ru-long XIE Li-sheng SHU 

机构地区：[1]School of Mathematical Sciences, University of Science and Technology of China [2]Department of Mathematics, Chaohu University [3]Department of Mathematics, Anhui Normal University

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第2期263-280,共18页应用数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (No.10371087);Natural Science Foundation of Education Committee of Anhui Province (No.KJ2011A138, No.KJ2012B116)

摘　　要：Let μ be a Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ（B（x,r）） ≤ Urn for all x∈Rd, r 〉 0 and for some fixed 0 〈 n 〈 d. In this paper, under this assumption, we prove that 0-type Calder6n-Zygmund operator which is bounded on L2 （μ） is also bounded from L^∞（μ） into RBMO （μ） and from Hb （μ） into L1（μ）. According to the interpolation theorem introduced by Tolsa, the LP（μ）-boundedness （1 〈 p 〈 ∞） is established for θ-type Calder6n-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type CMderθn-Zygmundoperator with RBMO （μ） function are bounded on LP（μ） （1 〈 p 〈 ∞）.Let μ be a Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ（B（x,r）） ≤ Urn for all x∈Rd, r 〉 0 and for some fixed 0 〈 n 〈 d. In this paper, under this assumption, we prove that 0-type Calder6n-Zygmund operator which is bounded on L2 （μ） is also bounded from L^∞（μ） into RBMO （μ） and from Hb （μ） into L1（μ）. According to the interpolation theorem introduced by Tolsa, the LP（μ）-boundedness （1 〈 p 〈 ∞） is established for θ-type Calder6n-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type CMderθn-Zygmundoperator with RBMO （μ） function are bounded on LP（μ） （1 〈 p 〈 ∞）.

关 键 词：non-doubling measure θ-type Calderón-Zygmund operator  commutators multilinear commuta-tors RBMO ( μ ) space H1 ∞atb ( μ ) space 

分 类 号：O177[理学—数学]