{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:KIV6BCK3OJLPP6DVLOZBJXACOD","short_pith_number":"pith:KIV6BCK3","schema_version":"1.0","canonical_sha256":"522be0895b7256f7f8755bb214dc0270fb7cf71935c696e334032c6e8416ffec","source":{"kind":"arxiv","id":"1110.0299","version":1},"attestation_state":"computed","paper":{"title":"On an Interesting Class of Variable Exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Yu. Karlovich, Ilya M. Spitkovsky","submitted_at":"2011-10-03T08:50:17Z","abstract_excerpt":"Let $\\mathcal{M}(\\mathbb{R}^n)$ be the class of functions $p:\\mathbb{R}^n\\to[1,\\infty]$ bounded away from one and infinity and such that the Hardy-Littlewood maximal function is bounded on the variable Lebesgue space $L^{p(\\cdot)}(\\mathbb{R}^n)$. We denote by $\\mathcal{M}^*(\\mathbb{R}^n)$ the class of variable exponents $p\\in\\mathcal{M}(\\mathbb{R}^n)$ for which $1/p(x)=\\theta/p_0+(1-\\theta)/p_1(x)$ with some $p_0\\in(1,\\infty)$, $\\theta\\in(0,1)$, and $p_1\\in\\mathcal{M}(\\mathbb{R}^n)$. Rabinovich and Samko \\cite{RS08} observed that each globally log-H\\\"older continuous exponent belongs to $\\math"},"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":"1110.0299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-03T08:50:17Z","cross_cats_sorted":[],"title_canon_sha256":"b6f5b7e255e416f5c03ee3da8db117f4ef159271cea9b47d5856e3e03904cb49","abstract_canon_sha256":"cf5a632b77ca13f4af7977d55ffdb461e7c98789776b3c86873868b8238d72a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:50.302605Z","signature_b64":"n6ez2OfOc/4jQNnWwo7fpNXy6ydQJ1SHyd3vfkpqMuFzStQLmmAzT5NPpUi3J8WWgxhxTgYro7kG1KDNLaFZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"522be0895b7256f7f8755bb214dc0270fb7cf71935c696e334032c6e8416ffec","last_reissued_at":"2026-05-18T04:11:50.302062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:50.302062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On an Interesting Class of Variable Exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Yu. Karlovich, Ilya M. Spitkovsky","submitted_at":"2011-10-03T08:50:17Z","abstract_excerpt":"Let $\\mathcal{M}(\\mathbb{R}^n)$ be the class of functions $p:\\mathbb{R}^n\\to[1,\\infty]$ bounded away from one and infinity and such that the Hardy-Littlewood maximal function is bounded on the variable Lebesgue space $L^{p(\\cdot)}(\\mathbb{R}^n)$. We denote by $\\mathcal{M}^*(\\mathbb{R}^n)$ the class of variable exponents $p\\in\\mathcal{M}(\\mathbb{R}^n)$ for which $1/p(x)=\\theta/p_0+(1-\\theta)/p_1(x)$ with some $p_0\\in(1,\\infty)$, $\\theta\\in(0,1)$, and $p_1\\in\\mathcal{M}(\\mathbb{R}^n)$. Rabinovich and Samko \\cite{RS08} observed that each globally log-H\\\"older continuous exponent belongs to $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0299","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":"1110.0299","created_at":"2026-05-18T04:11:50.302143+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.0299v1","created_at":"2026-05-18T04:11:50.302143+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0299","created_at":"2026-05-18T04:11:50.302143+00:00"},{"alias_kind":"pith_short_12","alias_value":"KIV6BCK3OJLP","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"KIV6BCK3OJLPP6DV","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"KIV6BCK3","created_at":"2026-05-18T12:26:32.869790+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/KIV6BCK3OJLPP6DVLOZBJXACOD","json":"https://pith.science/pith/KIV6BCK3OJLPP6DVLOZBJXACOD.json","graph_json":"https://pith.science/api/pith-number/KIV6BCK3OJLPP6DVLOZBJXACOD/graph.json","events_json":"https://pith.science/api/pith-number/KIV6BCK3OJLPP6DVLOZBJXACOD/events.json","paper":"https://pith.science/paper/KIV6BCK3"},"agent_actions":{"view_html":"https://pith.science/pith/KIV6BCK3OJLPP6DVLOZBJXACOD","download_json":"https://pith.science/pith/KIV6BCK3OJLPP6DVLOZBJXACOD.json","view_paper":"https://pith.science/paper/KIV6BCK3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.0299&json=true","fetch_graph":"https://pith.science/api/pith-number/KIV6BCK3OJLPP6DVLOZBJXACOD/graph.json","fetch_events":"https://pith.science/api/pith-number/KIV6BCK3OJLPP6DVLOZBJXACOD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KIV6BCK3OJLPP6DVLOZBJXACOD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KIV6BCK3OJLPP6DVLOZBJXACOD/action/storage_attestation","attest_author":"https://pith.science/pith/KIV6BCK3OJLPP6DVLOZBJXACOD/action/author_attestation","sign_citation":"https://pith.science/pith/KIV6BCK3OJLPP6DVLOZBJXACOD/action/citation_signature","submit_replication":"https://pith.science/pith/KIV6BCK3OJLPP6DVLOZBJXACOD/action/replication_record"}},"created_at":"2026-05-18T04:11:50.302143+00:00","updated_at":"2026-05-18T04:11:50.302143+00:00"}