{"paper":{"title":"Rational Approximation, Hardy Space - Decomposition of Functions in $L_p, p<1$: Further Results in Relation to Fourier Spectrum Characterization of Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guantie Deng, Tao Qian","submitted_at":"2015-03-29T11:04:07Z","abstract_excerpt":"Subsequent to our recent work on Fourier spectrum characterization of Hardy spaces $H^p(\\mathbb{R})$ for the index range $1\\leq p\\leq \\infty,$ in this paper we prove further results on rational Approximation, integral representation and Fourier spectrum characterization of functions in the Hardy  spaces $H^p(\\mathbb{R}), 0 < p\\leq \\infty,$ with particular interest in the index range $ 0< p \\leq 1.$ We show that the set of rational functions in $ H^p(\\mathbb{C}_{+1}) $ with the single pole $-i$ is dense in $ H^p(\\mathbb{C}_{+1}) $ for $0<p<\\infty.$ Secondly, for $0<p<1$, through rational functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08417","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"}