Weighted discrete Hardy's inequalities

  • Pascal Lefèvre University of Artois, Laboratoire de Mathématiques de Lens (LML), Lens, France
Keywords: Hardy's inequality, Cesàro mean, weight.

Abstract

UDC 517.5

We give a short proof of a weighted version of the discrete Hardy inequality. This includes the known case of classical monomial weights with optimal constant. The proof is based on the ideas of the short direct proof given recently in [P. Lefèvre, Arch. Math. (Basel), 114, № 2, 195–198 (2020)].

References

G. Bennett, Some elementary inequalities, Quart. J. Math. Oxford, 38, 401–425 (1987).

G. Curbera, W. Ricker, Spectrum of the Cesáro operator in $l^p$, Arch. Math. (Basel), 100, № 3, 267–271 (2013).

H. Hardy, J. E. Littlewood, G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, Cambridge (1967).

Y. C. Huang, Change of variable and discrete hardy inequality, preprint.

G. J. O. Jameson, R. Lashkaripour, Norms of certain operators on weighted $l^p$ spaces and Lorentz sequence spaces, J. Inequal. Pure and Appl. Math., 3, Issue 1 (2002).

F. Fischer, M. Keller, F. Pogorzelski, An improved discrete $p$-Hardy inequality}; ArXiv: 1910.03004.

A. Kufner, L. Maligranda, L. E. Persson, The prehistory of the Hardy inequality, Amer. Math. Monthly, 113, 715–732 (2006).

P. Lefèvre, A short direct proof of the discrete Hardy inequality, Arch. Math. (Basel), 114, № 2, 195–198 (2020).

P. Lefèvre, Weighted discrete Hardy's inequalities (unpublished)}; https://hal.archives-ouvertes.fr/hal-02528265.

Published
25.07.2023
How to Cite
LefèvreP. “Weighted Discrete Hardy’s Inequalities”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 7, July 2023, pp. 1009 -12, doi:10.37863/umzh.v75i7.7201.
Section
Short communications