{"paper":{"title":"More on the Density of Analytic Polynomials in Abstract Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Karlovich, Eugene Shargorodsky","submitted_at":"2017-11-23T20:45:24Z","abstract_excerpt":"Let $\\{F_n\\}$ be the sequence of the Fej\\'er kernels on the unit circle $\\mathbb{T}$. The first author recently proved that if $X$ is a separable Banach function space on $\\mathbb{T}$ such that the Hardy-Littlewood maximal operator $M$ is bounded on its associate space $X'$, then $\\|f*F_n-f\\|_X\\to 0$ for every $f\\in X$ as $n\\to\\infty$. This implies that the set of analytic polynomials $\\mathcal{P}_A$ is dense in the abstract Hardy space $H[X]$ built upon a separable Banach function space $X$ such that $M$ is bounded on $X'$. In this note we show that there exists a separable weighted $L^1$ spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08826","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"}