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Improvement of some discrete Hardy inequalities with variants
- Part of
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- Journal:
- Glasgow Mathematical Journal / Volume 67 / Issue 1 / January 2025
- Published online by Cambridge University Press:
- 25 November 2024, pp. 114-130
- Print publication:
- January 2025
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- Article
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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.
