{"paper":{"title":"Two Integral Sliding-Window Inequalities for Maximal Convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MG"],"primary_cat":"math.FA","authors_text":"Cheng Li, Gangsong Leng","submitted_at":"2026-06-09T07:50:21Z","abstract_excerpt":"We prove two sliding-window inequalities for maximal convolutions. The first concerns the multiplicative maximal convolution. If $f$ and $g$ are nonnegative continuous functions on $[0,A]$ and $[0,B]$, respectively, define \\[\n  h(x)=\\max_{\\substack{0\\le u\\le A\\\\0\\le x-u\\le B}} f(u)g(x-u),\\qquad 0\\le x\\le A+B. \\] Then there exists a window $[a,a+B]$ of length $B$ such that \\[\n  \\frac1B\\int_a^{a+B}h(x)\\,dx\\ge\n  \\left(\\frac1A\\int_0^A f(x)\\,dx\\right)\n  \\left(\\frac1B\\int_0^B g(x)\\,dx\\right). \\] The second concerns the additive maximal convolution. Let $f$ and $g$ be nonnegative continuous functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10518","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10518/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}