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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1812.11905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-12-31T17:24:13Z","cross_cats_sorted":[],"title_canon_sha256":"b886924db23e4925da49c82dd5049c606bfc11180d1ea725cdeccf3965f4a999","abstract_canon_sha256":"8d3d4dc848c4b1634a8f898688a1aab790da5c3a493abee9a606ae428a1dab3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:10.798183Z","signature_b64":"NRZm7dKRZqQxP3AGn3U8l/fNjZlE3Ae77ohfc9aw7p/02sr1OZ4UCOFY9ii0iW57OkiKwyxn1vkJf/LqzZVnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80bd5f391ced34bab9a04c2ac636f9cc2a5fb94b5916a6832fec96ab7aabde19","last_reissued_at":"2026-05-17T23:57:10.797797Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:10.797797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.11905","created_at":"2026-05-17T23:57:10.797859+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.11905v1","created_at":"2026-05-17T23:57:10.797859+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11905","created_at":"2026-05-17T23:57:10.797859+00:00"},{"alias_kind":"pith_short_12","alias_value":"QC6V6OI45U2L","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QC6V6OI45U2LVONA","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QC6V6OI4","created_at":"2026-05-18T12:32:46.962924+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QC6V6OI45U2LVONAJQVMMNXZZQ","json":"https://pith.science/pith/QC6V6OI45U2LVONAJQVMMNXZZQ.json","graph_json":"https://pith.science/api/pith-number/QC6V6OI45U2LVONAJQVMMNXZZQ/graph.json","events_json":"https://pith.science/api/pith-number/QC6V6OI45U2LVONAJQVMMNXZZQ/events.json","paper":"https://pith.science/paper/QC6V6OI4"},"agent_actions":{"view_html":"https://pith.science/pith/QC6V6OI45U2LVONAJQVMMNXZZQ","download_json":"https://pith.science/pith/QC6V6OI45U2LVONAJQVMMNXZZQ.json","view_paper":"https://pith.science/paper/QC6V6OI4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.11905&json=true","fetch_graph":"https://pith.science/api/pith-number/QC6V6OI45U2LVONAJQVMMNXZZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/QC6V6OI45U2LVONAJQVMMNXZZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QC6V6OI45U2LVONAJQVMMNXZZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QC6V6OI45U2LVONAJQVMMNXZZQ/action/storage_attestation","attest_author":"https://pith.science/pith/QC6V6OI45U2LVONAJQVMMNXZZQ/action/author_attestation","sign_citation":"https://pith.science/pith/QC6V6OI45U2LVONAJQVMMNXZZQ/action/citation_signature","submit_replication":"https://pith.science/pith/QC6V6OI45U2LVONAJQVMMNXZZQ/action/replication_record"}},"created_at":"2026-05-17T23:57:10.797859+00:00","updated_at":"2026-05-17T23:57:10.797859+00:00"}