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We prove a priori estimates of the following type :$$\\|\\Delta\\_{x}^{\\frac \\alpha 2} v \\|\\_{L^p({\\mathbb R}^N)} \\lec\\_p\\Big \\| L\\_{x } v  +  \\sum\\_{i,j=1}^{N}a\\_{ij}z\\_{i}\\partial\\_{z\\_{j}} v \\Big \\|\\_{L^p({\\mathbb R}^N)}, \\;\\; 1<p<\\infty,$$for $v \\in C\\_0^{\\infty}({\\mathbb R}^N)$,where $L\\_x$ is a non-local operator comparable with the ${\\mathbb R}^d $-fractional Laplacian $\\Delta\\_{x}^{\\frac \\alpha 2}$ in terms of symbols, $\\alpha \\in (0,2)$. We require that when $L\\_x$ is replaced by the classical ${\\mathbb R}^d$"},"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":"1607.08718","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-29T08:07:14Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"2bbfd0fda96d934ce031512f0e399f38804ccf4db70562ec213dd293db99e0c2","abstract_canon_sha256":"447903c3d09dd92bd63a62f6236447c98720232673582a7eb40ac096afa0b157"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:19.813063Z","signature_b64":"IFYeZUBUnuh14EywDknK+GPAjNyyq+C7iYwFUC/eCIPwC0jDw16jahjjfcApvr/y+1wHw7GqybdwhjqFWq+mCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae56299425468f9c2ca0c74324a7902c0a871541154758f745df77dbabde8dcb","last_reissued_at":"2026-05-18T00:44:19.812489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:19.812489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L^$p Estimates For Degenerate Non-Local Kolmogorov Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"E. Priola, L. Huang, S. Menozzi (LaMME)","submitted_at":"2016-07-29T08:07:14Z","abstract_excerpt":"Let $z = (x,y) \\in {\\mathbb R}^d \\times {\\mathbb R}^{N-d}$, with $1 \\le d < N$. We prove a priori estimates of the following type :$$\\|\\Delta\\_{x}^{\\frac \\alpha 2} v \\|\\_{L^p({\\mathbb R}^N)} \\lec\\_p\\Big \\| L\\_{x } v  +  \\sum\\_{i,j=1}^{N}a\\_{ij}z\\_{i}\\partial\\_{z\\_{j}} v \\Big \\|\\_{L^p({\\mathbb R}^N)}, \\;\\; 1<p<\\infty,$$for $v \\in C\\_0^{\\infty}({\\mathbb R}^N)$,where $L\\_x$ is a non-local operator comparable with the ${\\mathbb R}^d $-fractional Laplacian $\\Delta\\_{x}^{\\frac \\alpha 2}$ in terms of symbols, $\\alpha \\in (0,2)$. 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