{"paper":{"title":"The H\\\"ormander multiplier theorem I: The Linear Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Danqing He, Hanh Nguyen, Loukas Grafakos, Petr Honz\\'ik","submitted_at":"2016-07-09T15:02:51Z","abstract_excerpt":"We discuss $L^p(\\mathbb R^n)$ boundedness for Fourier multiplier operators that satisfy the hypotheses of the H\\\"ormander multiplier theorem in terms of an optimal condition that relates the distance $|\\frac 1p-\\frac12|$ to the smoothness $s$ of the associated multiplier measured in some Sobolev norm. We provide new counterexamples to justify the optimality of the condition $|\\frac 1p-\\frac12|<\\frac sn$ and we discuss the endpoint case $|\\frac 1p-\\frac12|=\\frac sn$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02620","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"}