Geodesic
Some new Hardy inequalities in probability
Filomat, Tome 37 (2023) no. 21, p. 7311

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DOI

Hardy et al. (1934) came up with Hardy's inequality in their book. Klaassen and Wellner (2021) gave the probability version of the Hardy inequality when the parameter p > 1. Based on their work, in this paper, we assign the randomness to variables as well. When p > 1, we give some extensions of Hardy's inequality. When 0 p 1, we provide the corresponding Hardy inequality in probability language. Also, we show that in some circumstances, our results contain the integral form of Hardy's inequality. We give a reversed Hardy inequality for random variables as well.
DOI : 10.2298/FIL2321311L
Classification : 60E05, 60G50
Keywords: Hardy’s inequality, Hölder’s inequality, Conditional expectation 
Dawei Lu; Qing Liu. Some new Hardy inequalities in probability. Filomat, Tome 37 (2023) no. 21, p. 7311 . doi: 10.2298/FIL2321311L
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     title = {Some new {Hardy} inequalities in probability},
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     doi = {10.2298/FIL2321311L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2321311L/}
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