{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VBMBV6LYQ7DO3QVITYMJ5ICXBB","short_pith_number":"pith:VBMBV6LY","schema_version":"1.0","canonical_sha256":"a8581af97887c6edc2a89e189ea057084af26bf5621589a7a6c7715d7b67a819","source":{"kind":"arxiv","id":"1612.07144","version":1},"attestation_state":"computed","paper":{"title":"$L^p$ mapping properties for nonlocal Schr\\\"odinger operators with certain potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Woocheol Choi, Yong-Cheol Kim","submitted_at":"2016-12-15T11:13:35Z","abstract_excerpt":"In this paper, we consider nonlocal Schr\\\"odinger equations with certain potentials $V$ given by an integro-differential operator $L_K$ as follows; \\begin{equation*}L_K u+V u=f\\,\\,\\text{ in $\\BR^n$ }\\end{equation*} where $V\\in\\rh^q$ for $q>\\f{n}{2s}$ and $0<s<1$. We denote the solution of the above equation by $\\cS_V f:=u$, which is called {\\it the inverse of the nonlocal Schr\\\"odinger operator $L_K+V$ with potential $V$}; that is, $\\cS_V=(L_K+V)^{-1}$. Then we obtain a weak Harnack inequality of weak subsolutions of the nonlocal equation \\begin{equation}\\begin{cases}L_K u+V u=0\\,\\,&\\text{ in "},"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":"1612.07144","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-15T11:13:35Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"10359197aa8cca42e87a70e146a3b9de716f428a9922312fd21c91dd8ad75437","abstract_canon_sha256":"b0ca9786fb65c9a1a96c5ccee7f87571e21b2079991d8a566d7f50c803fca18e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:14.585108Z","signature_b64":"V0JxHgSQPaYk6BiK6Ui3/BJJAPfm7IyngGzB/ado0f/pKq3Um1SbNHnG+pEuiv3wa5W/fC6im7SmOLNYpIpvAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8581af97887c6edc2a89e189ea057084af26bf5621589a7a6c7715d7b67a819","last_reissued_at":"2026-05-18T00:54:14.584673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:14.584673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L^p$ mapping properties for nonlocal Schr\\\"odinger operators with certain potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Woocheol Choi, Yong-Cheol Kim","submitted_at":"2016-12-15T11:13:35Z","abstract_excerpt":"In this paper, we consider nonlocal Schr\\\"odinger equations with certain potentials $V$ given by an integro-differential operator $L_K$ as follows; \\begin{equation*}L_K u+V u=f\\,\\,\\text{ in $\\BR^n$ }\\end{equation*} where $V\\in\\rh^q$ for $q>\\f{n}{2s}$ and $0<s<1$. We denote the solution of the above equation by $\\cS_V f:=u$, which is called {\\it the inverse of the nonlocal Schr\\\"odinger operator $L_K+V$ with potential $V$}; that is, $\\cS_V=(L_K+V)^{-1}$. 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