{"paper":{"title":"Smoothing estimates for non-dispersive equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Michael Ruzhansky, Mitsuru Sugimoto","submitted_at":"2015-08-03T15:16:57Z","abstract_excerpt":"This paper describes an approach to global smoothing problems for non-dispersive equations based on ideas of comparison principle and canonical transformation established in authors' previous paper, where dispersive equations were treated. For operators $a(D_x)$ of order $m$ satisfying the dispersiveness condition $\\nabla a(\\xi)\\neq0$ for $\\xi\\not=0$, the global smoothing estimate $$ \\|\\langle x\\rangle^{-s}|D_x|^{(m-1)/2}e^{ita(D_x)} \\varphi(x)\\|_{L^2(\\mathbb R_t\\times\\mathbb R^n_x)} \\leq C\\|\\varphi\\|_{L^2(\\mathbb R^n_x)} \\quad {\\rm(}s>1/2{\\rm)} $$ is well-known, while it is also known to fail"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00444","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":""},"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"}