{"paper":{"title":"Explicit constants in $L^p$-Hardy inequalities for Aharonov-Bohm potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Durvudkhan Suragan","submitted_at":"2026-07-14T11:58:32Z","abstract_excerpt":"For the two-dimensional Aharonov-Bohm potential $A_\\beta$ with flux $\\beta\\notin\\mathbb{Z}$ and $1<p<2$, Cazacu, Krej\\v{c}i\\v{r}\\'{\\i}k, Lam and Laptev proved by a compactness argument that their constant $\\lambda_\\beta(p)$ in the $L^p$-Hardy inequality strictly exceeds the free constant $\\big(\\tfrac{2-p}{p}\\big)^p$, and asked for a constructive proof with explicit estimates and for comparability of $\\lambda_\\beta(p)$ with a quantity depending on $\\text{dist}(\\beta,\\mathbb{Z})$. We answer both questions by using a compactness-free two-sided bound for the twisted angular constant. Our explicit "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12671","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12671/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}