## Annals of Functional Analysis

### Sharp weak estimates for Hardy-type operators

#### Abstract

In this article, we prove the weak bound for an $n$-dimensional Hardy operator on a central Morrey space. Meanwhile, we obtain the precise operator norm, and we give the weak bounds for the conjugate Hardy operator on Lebesgue space with power weights. The corresponding operator norms are also computed. As an application, we obtain an estimate for the gamma function.

#### Article information

Source
Ann. Funct. Anal., Volume 7, Number 3 (2016), 421-433.

Dates
Accepted: 28 December 2015
First available in Project Euclid: 17 June 2016

https://projecteuclid.org/euclid.afa/1466164867

Digital Object Identifier
doi:10.1215/20088752-3605447

Mathematical Reviews number (MathSciNet)
MR3513126

Zentralblatt MATH identifier
1346.42029

#### Citation

Gao, Guilian; Hu, Xiaomin; Zhang, Chunjie. Sharp weak estimates for Hardy-type operators. Ann. Funct. Anal. 7 (2016), no. 3, 421--433. doi:10.1215/20088752-3605447. https://projecteuclid.org/euclid.afa/1466164867

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