English

The two-weight Hardy inequality: a new elementary and universal proof

Classical Analysis and ODEs 2021-10-01 v1 Analysis of PDEs Functional Analysis

Abstract

We give a~new proof of the known criteria for the inequality \begin{equation*} \left(\int_{0}^{\infty}\left(\int_{0}^{t}f\right)^{q}w(t)\,dt\right)^{\frac{1}{q}} \leq C \left(\int_{0}^{\infty}f^{p}v\right)^{\frac{1}{p}}. \end{equation*} The innovation is in the elementary nature of the proof and its versatility.

Keywords

Cite

@article{arxiv.2109.15011,
  title  = {The two-weight Hardy inequality: a new elementary and universal proof},
  author = {Amiran Gogatishvili and Luboš Pick},
  journal= {arXiv preprint arXiv:2109.15011},
  year   = {2021}
}