{"paper":{"title":"A Note on Hardy Spaces and Bounded Operators","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Pablo Rocha","submitted_at":"2015-02-26T13:21:10Z","abstract_excerpt":"In this note we show that if f belongs to Hp(Rn)\\capLs(Rn), where 0 < p <= 1 < s < 1, then there exists a (p;infinite)-atomic decomposition which converges to f in Ls(Rn). From this fact, we prove that a bounded operator T on Ls(Rn) can be extended to a bounded operator from Hp(Rn) into Lp(Rn) if and only if T is bounded uniformly in Lp norm on all (p;infinite)-atoms. A similar result is also obtained from Hp(Rn) into Hp(Rn)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07542","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"}