A note on singular integral operators with non doubling measures

Abstract

Let $\mu$ be a Radon measure on $\rd$ which satisfies $\mu(B(x,\,r))\leq Cr^{n}$ for any $x\in \rd$ and $r>0$ and some fixed positive constants $C$ and $n$ with $0<n\leq d$. In this paper, the relationship between the $L^p(\mu)$ boundedness and certain weak type endpoint estimates are considered for the singular integral operators.