{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y5TYZPBUFQET7I7PK2EK6YQDCG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6f7bad03d8af0c7d13156e499404fbb51d2968aeec5ecd0dc28e8457309cfd60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-05T12:43:05Z","title_canon_sha256":"d817fa8cb23201e060b4fcedee73664a1f991ab80de8b86f9c8893605b4330a7"},"schema_version":"1.0","source":{"id":"1210.1738","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1738","created_at":"2026-05-18T03:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1738v2","created_at":"2026-05-18T03:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1738","created_at":"2026-05-18T03:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"Y5TYZPBUFQET","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y5TYZPBUFQET7I7P","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y5TYZPBU","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:08b9ec47fa96b3a7532acfd75a92f7ab922ee093de17ca3f48917e223be67ac7","target":"graph","created_at":"2026-05-18T03:15:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce Lorentz spaces $L_{p(\\cdot),q}(\\R^n)$ and $L_{p(\\cdot),q(\\cdot)}(\\R^n)$ with variable exponents. We prove several basic properties of these spaces including embeddings and the identity $L_{p(\\cdot),p(\\cdot)}(\\R^n)=L_{p(\\cdot)}(\\R^n)$. We also show that these spaces arise through real interpolation between $L_{\\p}(\\R^n)$ and $L_\\infty(\\R^n)$. Furthermore, we answer in a negative way the question posed in Diening, H\\\"ast\\\"o, and Nekvinda (2004) whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability.","authors_text":"Henning Kempka, Jan Vyb\\'iral","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-05T12:43:05Z","title":"Lorentz spaces with variable exponents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1738","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e3d2bd73e1d3d4bc238e1bffc433df5b42b4d3e253da061f6308a81ebc629d34","target":"record","created_at":"2026-05-18T03:15:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6f7bad03d8af0c7d13156e499404fbb51d2968aeec5ecd0dc28e8457309cfd60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-05T12:43:05Z","title_canon_sha256":"d817fa8cb23201e060b4fcedee73664a1f991ab80de8b86f9c8893605b4330a7"},"schema_version":"1.0","source":{"id":"1210.1738","kind":"arxiv","version":2}},"canonical_sha256":"c7678cbc342c093fa3ef5688af62031199fec3161b2464f1d3521c8b58be5aec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7678cbc342c093fa3ef5688af62031199fec3161b2464f1d3521c8b58be5aec","first_computed_at":"2026-05-18T03:15:06.424777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:06.424777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sO2lVuyRtR5PwQhi9HWJrN/Da7OKeZB+2tHtX+bS1qoHkXZV1+KUQhA/7F7BWeTPRQtDbD8+RqSvEGUfC0EdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:06.425655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1738","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3d2bd73e1d3d4bc238e1bffc433df5b42b4d3e253da061f6308a81ebc629d34","sha256:08b9ec47fa96b3a7532acfd75a92f7ab922ee093de17ca3f48917e223be67ac7"],"state_sha256":"773d92b3a37aec44379aea95df4e2e5605a1a7708cb52f843b2d3f33d383edac"}