{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FPOEMKNTQV5W6NEUGCHV5G6RGU","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":"5ebfd4badd8715e1b81c63ec51da8897036c1360505751d6270f8c849815a292","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-27T18:41:41Z","title_canon_sha256":"722a6c6799d58cf1c79da46427854f4752e5729cc91d0c02ace8d8a32a189233"},"schema_version":"1.0","source":{"id":"1807.10790","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10790","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10790v2","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10790","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"FPOEMKNTQV5W","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FPOEMKNTQV5W6NEU","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FPOEMKNT","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:34800c896c838cfc35101d3e21eea2a89a96ddf323ff8813dafe39c4f36adfb7","target":"graph","created_at":"2026-05-18T00:07:17Z","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":"In this work we present a newly developed study of the interpolation of weighted Sobolev spaces by the complex method. We show that in some cases, one can obtain an analogue of the famous Stein-Weiss theorem for weighted $L^{p}$ spaces. We consider an example which gives some indication that this may not be possible in all cases. Our results apply in cases which cannot be treated by methods in earlier papers about interpolation of weighted Sobolev spaces. They include, for example, a proof that $\\left[W^{1,p}(\\mathbb{R}^{d},\\omega_{0}),W^{1,p}(\\mathbb{R}^{d},\\omega_{1})\\right]_{\\theta}=W^{1,p}","authors_text":"Amit Einav, Michael Cwikel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-27T18:41:41Z","title":"Interpolation of weighted Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10790","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":"sha256:497fe9e4f6c4a54bc5aeba1b43674e4db2c1df0c45be1706f117f25361f0ca0a","target":"record","created_at":"2026-05-18T00:07:17Z","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":"5ebfd4badd8715e1b81c63ec51da8897036c1360505751d6270f8c849815a292","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-27T18:41:41Z","title_canon_sha256":"722a6c6799d58cf1c79da46427854f4752e5729cc91d0c02ace8d8a32a189233"},"schema_version":"1.0","source":{"id":"1807.10790","kind":"arxiv","version":2}},"canonical_sha256":"2bdc4629b3857b6f3494308f5e9bd13537c29b1721ca58ba63cf49907596512b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bdc4629b3857b6f3494308f5e9bd13537c29b1721ca58ba63cf49907596512b","first_computed_at":"2026-05-18T00:07:17.108304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:17.108304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rFAPuaHs9msrcQSB6NdxqtgbJCJSPEhsrbiw2Zov51uPZSGuksWSEz+K8a+tQxLP/a5xb8GqISZr+5HgxzYUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:17.108909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10790","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:497fe9e4f6c4a54bc5aeba1b43674e4db2c1df0c45be1706f117f25361f0ca0a","sha256:34800c896c838cfc35101d3e21eea2a89a96ddf323ff8813dafe39c4f36adfb7"],"state_sha256":"9fd21310702cbf312dd25daf6598e07394a43747ffaa895eb74a9c220edef7d6"}