{"paper":{"title":"Measures of polynomial growth and classical convolution inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Alex Iosevich, Ben Krause, Eric Sawyer, Ignacio Uriarte-Tuero, Krystal Taylor","submitted_at":"2014-10-06T16:14:37Z","abstract_excerpt":"We study $L^p(\\mu) \\to L^q(\\nu)$ mapping properties of the convolution operator $ T_{\\lambda}f(x)=\\lambda*(f\\mu)(x)$ and of the corresponding maximal operator $ {\\mathcal T}_{\\lambda}f(x)=\\sup_{t>0} |\\lambda_t*(f\\mu)(x)|$, where $\\lambda$ is a tempered distribution, and $\\mu$ and $\\nu$ are compactly supported measures satisfying the polynomial growth bounds $\\mu(B(x,r)) \\leq Cr^{s_{\\mu}}$ and $\\nu(B(x,r)) \\leq Cr^{s_{\\nu}}$. As a result, we prove variants of the classical $L^p$-improving (Littman; Strichartz) and maximal (Stein) inequalities in a setting where the Plancherel formula is not ava"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1436","kind":"arxiv","version":2},"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"}