An elementary approach to integral inequalities involving higher order derivatives
Classical Analysis and ODEs
2025-09-19 v1 Spectral Theory
Abstract
Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven by elementary means. It is then shown how this framework generalizes the notions of Hardy improving potentials and Bessel pairs. Numerous examples of inequalities both new and previously known in the literature are given that may be proven in this manner.
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Cite
@article{arxiv.2509.14513,
title = {An elementary approach to integral inequalities involving higher order derivatives},
author = {Bart Rosenzweig and Jonathan Stanfill},
journal= {arXiv preprint arXiv:2509.14513},
year = {2025}
}
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15 pages