{"paper":{"title":"Vector-valued Hilbert transforms along curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guixiang Hong, Honghai Liu","submitted_at":"2014-03-02T09:32:52Z","abstract_excerpt":"In this paper, we show that Hilbert transforms along some curves are bounded on $L^p({\\mathbb R}^n;X)$ for some $1<p<\\infty$ and some UMD spaces $X$. In particular, we prove that the Hilbert transform along some curves are completely $L^p$-bounded in the terminology from operator space theory. Moreover, we obtain the $L^p(\\mathbb{R}^n;X)$-boundedness of anisotropic singular integrals by using the \"method of rotations\" of Calder\\'{o}n-Zygmund.\n  All these results extend the existing related ones."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0177","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":""},"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"}