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## Weighted norm inequalities for maximal singular integrals with nondoubling measures

### Tom 187 / 2008

Studia Mathematica 187 (2008), 101-123 MSC: 42B20, 43A99. DOI: 10.4064/sm187-2-1

#### Streszczenie

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 ${\varrho,p\in [1,\infty)}$.

#### Autorzy

• Guoen HuDepartment of Applied Mathematics
University of Information Engineering
P.O. Box 1001-747
Zhengzhou 450002
People's Republic of China
e-mail
• Dachun YangSchool of Mathematical Sciences
Beijing Normal University
Laboratory of Mathematics and Complex Systems
Ministry of Education
Beijing 100875
People's Republic of China
e-mail

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