×

Sharp weak estimates for Hardy-type operators. (English) Zbl 1346.42029

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.

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
PDFBibTeX XMLCite
Full Text: DOI Euclid