Gao, Guilian; Hu, Xiaomin; Zhang, Chunjie Sharp weak estimates for Hardy-type operators. (English) Zbl 1346.42029 Ann. Funct. Anal. 7, No. 3, 421-433 (2016). Summary: In this article, we prove a weak bound for an \(n\)-dimensional Hardy operator on a central Morrey space. Meanwhile, we obtain the precise operator norm, and we give weak bounds for the conjugate Hardy operator on a Lebesgue space with power weights. The corresponding operator norms are also computed. As an application, we obtain an estimate for the gamma function. Cited in 6 Documents MSC: 42B99 Harmonic analysis in several variables 42B35 Function spaces arising in harmonic analysis 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 26D10 Inequalities involving derivatives and differential and integral operators 26D15 Inequalities for sums, series and integrals 33B15 Gamma, beta and polygamma functions Keywords:Hardy operator; conjugate Hardy operator; central Morrey spaces; weak central Morrey spaces; duality; gamma function PDFBibTeX XMLCite \textit{G. Gao} et al., Ann. Funct. Anal. 7, No. 3, 421--433 (2016; Zbl 1346.42029) Full Text: DOI Euclid