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Optimal Hardy Inequalities for Fractional p-Laplacians on the Integers
Abstract
We obtain optimal Hardy inequalities for fractional powers of the p-Laplacian Δpσ on ℤ, p∈ (1,∞), σ∈ (0, 1/p). Asymptotically, the optimal weights behave like |x|−pσ as |x|→ ∞. We show a similar result for the Riesz fractional p-Laplacian. In an appendix, we show that for general p-Laplace operators on locally summable graphs, p-null-criticality implies p-optimality at infinity.
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BibTeX
@misc{fischer2026optimal,
title = {{Optimal Hardy Inequalities for Fractional $p$-Laplacians on the Integers}},
author = {Florian Fischer and Marius Nietschmann},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37336},
eprint = {2609.37336},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05779464v1},
}
RIS
TY - UNPB
TI - Optimal Hardy Inequalities for Fractional p-Laplacians on the Integers
AU - Florian Fischer
AU - Marius Nietschmann
PY - 2026
DA - 2026/09/29
PB - HAL
DO - 10.48550/arxiv.2609.37336
UR - https://hal.science/hal-05779464v1
AB - We obtain optimal Hardy inequalities for fractional powers of the p-Laplacian Δ_p^σ on ℤ, p∈ (1,∞), σ∈ (0, 1/p). Asymptotically, the optimal weights behave like |x|^−pσ as |x|→ ∞. We show a similar result for the Riesz fractional p-Laplacian. In an appendix, we show that for general p-Laplace operators on locally summable graphs, p-null-criticality implies p-optimality at infinity.
ER -