{"paper":{"title":"Sub-Hardy Hilbert spaces on the circle and torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ajay Kumar, Dinesh Singh, Niteesh Sahni","submitted_at":"2013-10-24T13:58:32Z","abstract_excerpt":"Sahni and Singh settled a problem posed by Yousefi & Hesameddini by generalizing their main result with a simple proof in the setting of sub-Hilbert spaces in $H^2(T)$. In this paper, we extend the main result of Sahni and Singh to the setting of the Banach spaces $H^p$, $1\\le p\\le\\infty$ on the circle and the torus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6619","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"}