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

Let μ be a Radon measure on R~d which may be non-doubling.The only condition satisfiedby 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,theauthors prove that the boundedness from H~1(μ) into L(μ) of a singular integral operator T withCalderón-Zygmund kernel of Hrmander type implies its L~2(μ)-boundedness.