Annals of Functional Analysis

Sharp weak estimates for Hardy-type operators

Guilian Gao, Xiaomin Hu, and Chunjie Zhang

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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

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

Received: 4 August 2015
Accepted: 28 December 2015
First available in Project Euclid: 17 June 2016

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Zentralblatt MATH identifier

Primary: 42B35: Function spaces arising in harmonic analysis
Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 26D15: Inequalities for sums, series and integrals

Hardy operator the conjugate Hardy operator central Morrey space weak central Morrey space duality


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.

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