On Hardy q-inequalities
Classical Analysis and ODEs
2014-03-26 v1
Abstract
Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.
Keywords
Cite
@article{arxiv.1403.6292,
title = {On Hardy q-inequalities},
author = {Lech Maligranda and Ryskul Oinarov and Lars-Erik Persson},
journal= {arXiv preprint arXiv:1403.6292},
year = {2014}
}
Comments
To appear in Czechoslovak Math. J., 22 pages