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This result is then applied to show that $(\\widetilde{L^p},L^{\\infty})$ is a Calder\\'on couple for $1\\leq p<\\infty $, where $\\widetilde{L^{p}}$ is the K\\\"othe dual of the Ces\\`aro space $Ces_{p'}$ (or equivalently the down space $L^{p'}_{\\downarrow}$). In particular, $(\\widetilde{L^1},L^{\\infty})$"},"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":"1502.04882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-17T13:12:28Z","cross_cats_sorted":[],"title_canon_sha256":"9fdb66007a5770cc00bf1cffe3fa1d7fd5919fb5612275df034b8b610ed13fc6","abstract_canon_sha256":"1aacf6ad52e6fec947f71e2e067cbb9d47d9eb08edd3e5b2f469768f8c417430"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:53.637416Z","signature_b64":"LPmtEO8DWd8cd+4uEFj48zHjf4zWwIvGXlAylZznkQCvex3aWXoT2iIHzbF7cJpXXscXRu/Gwa5GDi3nQ/83Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68bd6fe0674e907c4fce73605bae1c36c2180f9dd377f6c23a84d1eb30ee69e6","last_reissued_at":"2026-05-18T02:26:53.636857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:53.636857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monotone substochastic operators and a new Calderon couple","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Karol Lesnik","submitted_at":"2015-02-17T13:12:28Z","abstract_excerpt":"An important result on submajorization, which goes back to Hardy, Littlewood and P\\'olya, states that $b\\preceq a$ if and only if there is a doubly stochastic matrix $A$ such that $b=Aa$. 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