Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 3 (2016), 421-433.
Sharp weak estimates for Hardy-type operators
In this article, we prove the weak bound for an -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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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