{"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 $b=Aa$. We prove that under monotonicity assumptions on vectors $a$ and $b$ respective matrix $A$ may be chosen monotone. 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, $(\\widetilde{L^1},L^{\\infty})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04882","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}