Weighted norm inequalities for maximal singular integrals with nondoubling measures
Volume 187 / 2008
Studia Mathematica 187 (2008), 101-123
MSC: 42B20, 43A99.
DOI: 10.4064/sm187-2-1
Abstract
Let $\mu$ be a nonnegative Radon measure on ${{{\mathbb R}}^d}$ which satisfies $\mu(B(x,r)) \le Cr^n$ for any $x\in {{{\mathbb R}}^d}$ and $r>0$ and some positive constants $C$ and $n\in (0, d]$. In this paper, some weighted norm inequalities with $A_p^\varrho(\mu)$ weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure $\mu$, via certain weighted estimates with $A_{\infty}^\varrho(\mu)$ weights of Muckenhoupt type involving the John–Strömberg maximal operator and the John–Strömberg sharp maximal operator, where ${\varrho,p\in [1,\infty)}$.
