Weighted norm inequalities for maximal singular integrals with nondoubling measures

Guoen Hu¹ ; Dachun Yang²

¹Department of Applied Mathematics University of Information Engineering P.O. Box 1001-747 Zhengzhou 450002 People's Republic of China
²School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 People's Republic of China

Studia Mathematica, Tome 187 (2008) no. 2, pp. 101-123

Résumé

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

Détail

DOI : 10.4064/sm187-2-1

Keywords: nonnegative radon measure mathbb which satisfies mathbb positive constants paper weighted norm inequalities varrho weights muckenhoupt type obtained maximal singular integral operators measure via certain weighted estimates infty varrho weights muckenhoupt type involving john str mberg maximal operator john str mberg sharp maximal operator where varrho infty