{"paper":{"title":"Multivariate H\\\"ormander-type multiplier theorem for the Hankel transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B{\\l}a\\.zej Wr\\'obel, Jacek Dziuba\\'nski, Marcin Preisner","submitted_at":"2011-10-11T12:30:02Z","abstract_excerpt":"Let H(f)(x)=\\int_{(0,infty)^d} f(v) E_{x}(v) d\\nu(v), be the multivariable Hankel transform, where E_{x}(v)=\\prod_{k=1}^d (x_k v_k)^{-a_k+1/2} J_{a_k-1/2}(x_k v_k), d\\nu(v)=v^a dv, a=(a_1,...,a_d). We give sufficient conditions on a bounded continuous function m(v) which guarantee that the operator H(m Hf) is bounded on L^p(d\\nu) and of weak-type (1,1), or bounded on the Hardy space H^1((0,infty)^d, d\\nu) in the sense of Coifman-Weiss."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2348","kind":"arxiv","version":2},"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"}