{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PKFTBC4S47CAVEGG232RL5W52U","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":"8242d54f910b72638f54a2d69a1d3481528cf36cc6b2b38b00f33cec846dd24e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-23T15:10:31Z","title_canon_sha256":"7af3afde1157af4741b6955945854a04d75bda8cf0f73ca0e7f3a0737aac3259"},"schema_version":"1.0","source":{"id":"1905.09703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.09703","created_at":"2026-05-17T23:45:16Z"},{"alias_kind":"arxiv_version","alias_value":"1905.09703v1","created_at":"2026-05-17T23:45:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09703","created_at":"2026-05-17T23:45:16Z"},{"alias_kind":"pith_short_12","alias_value":"PKFTBC4S47CA","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PKFTBC4S47CAVEGG","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PKFTBC4S","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:bb1ed4ee523c7cdf0a746b7a55882c7deb5e5197d1c44db308e889da386bf485","target":"graph","created_at":"2026-05-17T23:45:16Z","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 study embeddings of Besov-Morrey spaces ${\\cal N}^{s}_{u,p,q}}({\\mathbb R}^d)$ and of Triebel-Lizorkin-Morrey spaces ${\\cal E}^{s}_{u,p,q}}({\\mathbb R}^d)$ in the limiting cases when the smoothness $s$ equals $s_0=d\\max(1/u-p/u,0)$ or $s_{\\infty}=d/u$, which is related to the embeddings in $L_1^{loc}({\\mathbb R}^d)$ or in $L_\\infty({\\mathbb R}^d)$, respectively. When $s=s_0$ we characterise the embeddings in $L_1^{loc}({\\mathbb R}^d)$ and when $s=s_{\\infty}$ we obtain embeddings into Orlicz-Morrey spaces of exponential type and into generalised Morrey spaces.","authors_text":"Dorothee D. Haroske, Leszek Skrzypczak, Susana D. Moura","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-23T15:10:31Z","title":"Some embeddings of Morrey spaces with critical smoothness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09703","kind":"arxiv","version":1},"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":"sha256:0df2f0fb7d951f2f2e5f4a36b3a427ec1df777f1aeeb004148677361b375c10d","target":"record","created_at":"2026-05-17T23:45:16Z","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":"8242d54f910b72638f54a2d69a1d3481528cf36cc6b2b38b00f33cec846dd24e","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-23T15:10:31Z","title_canon_sha256":"7af3afde1157af4741b6955945854a04d75bda8cf0f73ca0e7f3a0737aac3259"},"schema_version":"1.0","source":{"id":"1905.09703","kind":"arxiv","version":1}},"canonical_sha256":"7a8b308b92e7c40a90c6d6f515f6ddd51fa719ffc9bb08ed7e0b3087e4f0445d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a8b308b92e7c40a90c6d6f515f6ddd51fa719ffc9bb08ed7e0b3087e4f0445d","first_computed_at":"2026-05-17T23:45:16.281797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:16.281797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1knVqIZs8WUJy5p9cT51jELotpX+kOEQeMVz+jxgbJ5dyznyS6/3rNI76tEwotEEvquSO/gO6OZNTgnUaQinAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:16.282231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.09703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0df2f0fb7d951f2f2e5f4a36b3a427ec1df777f1aeeb004148677361b375c10d","sha256:bb1ed4ee523c7cdf0a746b7a55882c7deb5e5197d1c44db308e889da386bf485"],"state_sha256":"db3198d1ab429195920b9bca54252dfb24af38204afbc92c1d58838b9925677b"}