{"paper":{"title":"$L^p$-estimates for the 2D wave equation in the scaling-critical magnetic field","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fang Zhang, Jialu Wang, Jiqiang Zheng, Junyong Zhang","submitted_at":"2025-02-05T13:22:37Z","abstract_excerpt":"In this paper, we study the $L^{p}$-estimates for the solution to the $2\\mathrm{D}$-wave equation with a scaling-critical magnetic potential. Inspired by the work of \\cite{FZZ}, we show that the operators $(I+\\mathcal{L}_{\\mathbf{A}})^{-\\gamma}e^{it\\sqrt{\\mathcal{L}_{\\mathbf{A}}}}$ is bounded in $L^{p}(\\mathbb{R}^{2})$ for $1<p<+\\infty$ when $\\gamma>|1/p-1/2|$ and $t>0$, where $\\mathcal{L}_{\\mathbf{A}}$ is a magnetic Schr\\\"odinger operator. In particular, we derive the $L^{p}$-bounds for the sine wave propagator $\\sin(t\\sqrt{\\mathcal{L}_{\\mathbf{A}}})\\mathcal{L}^{-\\frac12}_{\\mathbf{A}}$. The k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03151","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/2502.03151/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"}