A Remark on the Boundedness of Calder6n-Zygmund Operators in Non-homogeneous Spaces  

作　　者：Xiao Li FU Guo En HU Da Chun YANG 

机构地区：[1]School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China [2]Department of Applied Mathematics, University of Information Engineering, Zhengzhou 450002, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第3期449-456,共8页数学学报（英文版）

基　　金：NNSF(No.10271015)of China;RFDP(No.20020027004)of China

摘　　要：Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the boundedness from H^1（μ） into L^1,∞ （μ） of a singular integral operator T with Calderón-Zygmund kernel of HSrmander type implies its L^2（μ）-boundedness.Let μ be a Radon measure on R^d which may be non-doubling. The only condition satisfied by μ is that μ（B（x,r）） ≤ Cr^n for all x∈R^d r 〉 0 and some fixed 0 〈 n ≤ d. In this paper, the authors prove that the boundedness from H^1（μ） into L^1,∞ （μ） of a singular integral operator T with Calderón-Zygmund kernel of HSrmander type implies its L^2（μ）-boundedness.

关 键 词：Caldern-Zygmund operator Hardy space L^1 ∞（μ） Non-doubling measure 

分 类 号：O174.12[理学—数学]