English

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

R2 v1 2026-06-22T03:33:49.247Z