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

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 Calderon-Zygmund kernel of Hoermander type implies its L~2(μ)-boundedness.