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We obtain the estimate for the corner points $P,P'$."},"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":"1601.07643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-28T04:44:49Z","cross_cats_sorted":[],"title_canon_sha256":"435c9d7dd8afc3c2a01586e879b3a5050eab1b251ad1b9bc43a6cb2ef4fcfdfb","abstract_canon_sha256":"bc9c60bbec5efb0d536f61225d70833a693175ed2661a9c0c1f6c78c7add39e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:24.344238Z","signature_b64":"+doD43veQj4BaLc9dUxgj4FeeNb+4+iVDdv+Kn1XYt3YDn7DS7v5GUKOGNpghTJSEmzc+TzrXahCAZt3/ptkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c5b8182ed133187d4d9020cfb89c49e499355c69ab2e598edefad96b8a7bc7b","last_reissued_at":"2026-05-18T01:16:24.343671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:24.343671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inhomogeneous Strichartz estimates for Schr\\\"odinger's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ihyeok Seo, Youngwoo Koh","submitted_at":"2016-01-28T04:44:49Z","abstract_excerpt":"Foschi and Vilela in their independent works (\\cite{F},\\cite{V}) showed that the range of $(1/r,1/\\widetilde{r})$ for which the inhomogeneous Strichartz estimate $ \\big\\|\\int_{0}^{t}e^{i(t-s)\\Delta}F(\\cdot,s)ds\\big\\|_{L^{q}_tL^{r}_x} \\lesssim \\|F\\|_{L^{\\widetilde{q}'}_tL^{\\widetilde{r}'}_x} $ holds for some $q,\\widetilde{q}$ is contained in the closed pentagon with vertices $A,B,B',P,P'$ except the points $P,P'$ (see Figure 1). 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