Geodesic
Improvement of some discrete Hardy inequalities with variants
Glasgow mathematical journal, Tome 67 (2025) no. 1, pp. 114-130

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DOI

In this paper, we establish a new version of one-dimensional discrete improved Hardy’s inequality with shifts by introducing a shifting discrete Dirichlet’s Laplacian. We prove that the general discrete Hardy’s inequality as well as its variants in some special cases admit improvements. Further, it is proved that two-variable discrete $p$-Hardy inequality can also be improved via improved discrete $p$-Hardy inequality in one dimension. The result is also extended to the multivariable cases.
DOI : 10.1017/S0017089524000296
Mots-clés : Hardy’s inequality, Variant Hardy’s inequality, Improvement, Double sequence and series, Multivariable series 
Das, Bikram; Chakraborty, S. K.; Sadhu, Rudrajit; Manna, Atanu. Improvement of some discrete Hardy inequalities with variants. Glasgow mathematical journal, Tome 67 (2025) no. 1, pp. 114-130. doi: 10.1017/S0017089524000296
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     title = {Improvement of some discrete {Hardy} inequalities with variants},
     journal = {Glasgow mathematical journal},
     pages = {114--130},
     year = {2025},
     volume = {67},
     number = {1},
     doi = {10.1017/S0017089524000296},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089524000296/}
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