Affiliation:
1. School of Mathematical Sciences, Dalian University of Technology, Dalian, China
Abstract
Hardy et al. (1934) came up with Hardy?s inequality in their book. Klaassen
andWellner (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.
Publisher
National Library of Serbia
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