{"paper":{"title":"On Calder\\'on's conjecture","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Christoph Thiele, Michael Lacey","submitted_at":"1999-03-01T00:00:00Z","abstract_excerpt":"This paper is a successor of \\cite{laceyt}. In that paper we considered bilinear operators of the form\n  H_alpha(f_1,f_2)(x) = p.v. \\int f_1(x-t) f_2(x + alpha t)/t dt,\n  which are originally defined for f_1, f_2 in the Schwartz class S(R). The natural question is whether estimates of the form\n  H_alpha(f_1,f_2)|_p <= C_{alpha,p_1,p_2} |f_1|_{p_1} |f_2|_{p_2}\n  with constants C_{alpha,p_1,p_2} depending only on alpha,p_1,p_2 and p = p_1p_2/(p_1+p_2) hold. The purpose of the current paper is to extend the range of exponents p_1 and p_2 for which the estimate is known. In particular, the case p_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9903203","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"}