{"paper":{"title":"Asymptotic behavior of $L^p$ estimates for a class of multipliers with homogeneous unimodular symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Aleksandar Bulj, Vjekoslav Kova\\v{c}","submitted_at":"2022-03-08T12:06:08Z","abstract_excerpt":"We study Fourier multiplier operators associated with symbols $\\xi\\mapsto \\exp(i\\lambda\\phi(\\xi/|\\xi|))$, where $\\lambda$ is a real number and $\\phi$ is a real-valued $C^\\infty$ function on the standard unit sphere $\\mathbb{S}^{n-1}\\subset\\mathbb{R}^n$. For $1<p<\\infty$ we investigate asymptotic behavior of norms of these operators on $L^p(\\mathbb{R}^n)$ as $|\\lambda|\\to\\infty$. We show that these norms are always $O((p^\\ast-1) |\\lambda|^{n|1/p-1/2|})$, where $p^\\ast$ is the larger number between $p$ and its conjugate exponent. More substantially, we show that this bound is sharp in all even-d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.04035","kind":"arxiv","version":3},"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/2203.04035/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"}