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Our result improves \\cite[Theorem 1.3]{BM} by A.\\ Bendikov and P.\\ Maheux for fractional powers, and it also holds for non-symmetric settings. As an application, we will derive hypercontractivity, supercontractivity and ultracontractivity of subordinate semigroups."},"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":"1105.3082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-16T12:47:19Z","cross_cats_sorted":[],"title_canon_sha256":"9a72970140746c85db6447f9a7b38bc6f0905f66bdef04a4202185848135b5b5","abstract_canon_sha256":"beccedcf31b00018523cedcc88488bba639183515bf3f5452c488e2e01e60668"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:01.423202Z","signature_b64":"uGITqGOT/l+mM/oBGRJtLsyAtJ5VbH/PN9S9qD3rVt5syaVgCIk/yUiYUSm9l2IJ/+2jPsN+oI63KAke0kHOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62584f7fad027561c4a0d3ff3b34073cb5fac8ae6133f27ec2e0558f7cfe149f","last_reissued_at":"2026-05-18T04:22:01.422736Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:01.422736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional Inequalities and Subordination: Stability of Nash and Poincar\\'e inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Ren\\'e L. 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