Fractional and non-fractional Hardy inequality on a lattice $\Z^d$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908409166561280 |
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| author | Dyda, Bartłomiej |
| author_facet | Dyda, Bartłomiej |
| contents | We present simple proofs of a discrete fractional and non-fractional Hardy inequality, Our constants are explicit, but not optimal. In the class of power weights, we get a complete picture of when the non-fractional Hardy inequality holds, for any dimension $d$ of the lattice $\Z^d$ and exponent $0<p<\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional and non-fractional Hardy inequality on a lattice $\Z^d$ Dyda, Bartłomiej Functional Analysis Primary 26D15, secondary 26A33, 35J05 We present simple proofs of a discrete fractional and non-fractional Hardy inequality, Our constants are explicit, but not optimal. In the class of power weights, we get a complete picture of when the non-fractional Hardy inequality holds, for any dimension $d$ of the lattice $\Z^d$ and exponent $0<p<\infty$. |
| title | Fractional and non-fractional Hardy inequality on a lattice $\Z^d$ |
| topic | Functional Analysis Primary 26D15, secondary 26A33, 35J05 |
| url | https://arxiv.org/abs/2506.08273 |