{"paper":{"title":"On the orthogonal democratic systems in the $L^p$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. San Antolin, K.S. Kazarian","submitted_at":"2018-12-31T17:24:13Z","abstract_excerpt":"The concept of bidemocratic pair for a Banach space was introduced in \\cite{KS:18}. We construct a family of orthonormal systems $\\mathfrak{F}_{l},$ $l\\in (0,\\infty)$ of functions defined on $[-1,1]$ such that the pair $(\\mathfrak{F}_{l},\\mathfrak{F}_{l})$ is bidemocratic for $L^{p}[-1,1]$ and for $L^{p'}[-1,1]$ if $l\\in (0, \\frac{p}{2(p-2)}]$, where $p>2$ and $p'= \\frac{p}{p-1}$. The system $\\mathfrak{F}_{l}$ is not democratic for $L^{p'}[-1,1]$ when $l\\in (\\frac{p}{2(p-2)}, \\frac{p}{p-2}). $ When $l> \\frac{p}{2(p-2)}$ the pair $(\\mathfrak{F}_{l},\\mathfrak{F}_{l})$ is not bidemocratic neither"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11905","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"}