{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SUYBSNNU5B6VBHJHVMTAWTSC4U","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":"dab8fc641dd5dade54d2f24d44e093c27ae4e60d897c0cf97781ef20fd8f60e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-06T10:17:13Z","title_canon_sha256":"f00e0b4806e9dff785a15d67815fb78152676e99747953c3fd79d28958fe60b7"},"schema_version":"1.0","source":{"id":"1511.02020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02020","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02020v1","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02020","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"SUYBSNNU5B6V","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SUYBSNNU5B6VBHJH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SUYBSNNU","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:6009aebe028340712852914418f9ecb08fdbfe1151649c973c3928e8b895d1ba","target":"graph","created_at":"2026-05-18T01:27:38Z","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":"The generalized Morrey space was defined independetly by T. Mizuhara 1991 and E. Nakai in 1994. Generalized Morrey space ${\\mathcal M}_{p,\\phi}({\\mathbb R}^n)$ is equipped with a parameter $0<p<\\infty$ and a function $\\phi:{\\mathbb R}^n \\times (0,\\infty) \\to (0,\\infty)$. Our experience shows that ${\\mathcal M}_{p,\\phi}({\\mathbb R}^n)$ is easy to handle when $1<p<\\infty$. However, when $0<p \\le 1$, the function space ${\\mathcal M}_{p,\\phi}({\\mathbb R}^n)$ is difficult to handle as many examples show.\n  The aim of this paper is twofold. One of them is to propose a way to deal with ${\\mathcal M}_","authors_text":"Ali Akbulut, Takahiro Noi, Vagif Guliyev, Yoshihiro Sawano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-06T10:17:13Z","title":"Generalized Hardy-Morrey spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02020","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":"sha256:83b4052b2be1384a7598e8cc3e4971455623b1b3525997c5b45fc5ce173d3f16","target":"record","created_at":"2026-05-18T01:27:38Z","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":"dab8fc641dd5dade54d2f24d44e093c27ae4e60d897c0cf97781ef20fd8f60e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-06T10:17:13Z","title_canon_sha256":"f00e0b4806e9dff785a15d67815fb78152676e99747953c3fd79d28958fe60b7"},"schema_version":"1.0","source":{"id":"1511.02020","kind":"arxiv","version":1}},"canonical_sha256":"95301935b4e87d509d27ab260b4e42e53c0ae15932e46240e5d06b803fd7bcd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95301935b4e87d509d27ab260b4e42e53c0ae15932e46240e5d06b803fd7bcd4","first_computed_at":"2026-05-18T01:27:38.056071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:38.056071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ADiFIzV6/ug02Cp3NmtED9fsPEXCm6KdN93PdMiV2GjAluhhr1PvqsPl4RN+t4DKNwwaKY2PXcoLogMFq3MUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:38.056744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83b4052b2be1384a7598e8cc3e4971455623b1b3525997c5b45fc5ce173d3f16","sha256:6009aebe028340712852914418f9ecb08fdbfe1151649c973c3928e8b895d1ba"],"state_sha256":"fbdb1ed0d47b099b38ad242ee21917e7a5b9f4875fc2bc5aa6c958bede32abc4"}