An elementary approach to integral inequalities involving higher order derivatives
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908545366097920 |
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| author | Rosenzweig, Bart Stanfill, Jonathan |
| author_facet | Rosenzweig, Bart Stanfill, Jonathan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14513 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An elementary approach to integral inequalities involving higher order derivatives Rosenzweig, Bart Stanfill, Jonathan Classical Analysis and ODEs Spectral Theory Primary: 26D10, 34B30, 47A30, Secondary: 34B24, 34C10, 34L15 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. |
| title | An elementary approach to integral inequalities involving higher order derivatives |
| topic | Classical Analysis and ODEs Spectral Theory Primary: 26D10, 34B30, 47A30, Secondary: 34B24, 34C10, 34L15 |
| url | https://arxiv.org/abs/2509.14513 |