## Taiwanese Journal of Mathematics

### A NOTE ON WEIGHTED NORM INEQUALITIES FOR FRACTIONAL MAXIMAL OPERATORS WITH NON-DOUBLING MEASURES

#### Abstract

Let $\mu$ be a non-negative Borel measure on $\mathbb{R}^d$ which only satisfies some growth condition, we study two-weight norm inequalities for fractional maximal functions associated to such $\mu$. A necessary and sufficient condition for the maximal operator to be bounded from $L^p(v)$ into weak $L^{q}(u)$ $(1 \leq p \leq q \lt \infty)$ is given. Furthermore, by using certain Orlicz norm, a strong type inequality is obtained.

#### Article information

Source
Taiwanese J. Math., Volume 16, Number 4 (2012), 1409-1422.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406741

Digital Object Identifier
doi:10.11650/twjm/1500406741

Mathematical Reviews number (MathSciNet)
MR2951145

Zentralblatt MATH identifier
1266.42050

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory

#### Citation

Wang, Weihong; Tan, Chaoqiang; Lou, Zengjian. A NOTE ON WEIGHTED NORM INEQUALITIES FOR FRACTIONAL MAXIMAL OPERATORS WITH NON-DOUBLING MEASURES. Taiwanese J. Math. 16 (2012), no. 4, 1409--1422. doi:10.11650/twjm/1500406741. https://projecteuclid.org/euclid.twjm/1500406741

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