{"paper":{"title":"Dilation-commuting operators on power-weighted Orlicz classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rajesh K. Singh, Rama Rawat, Ron Kerman","submitted_at":"2017-08-04T12:55:20Z","abstract_excerpt":"Let $\\Phi_1$ and $\\Phi_2$ be nondecreasing functions from $\\mathbb{R_+}=(0,\\infty)$ onto itself. For $i=1,2$ and $\\gamma \\in \\mathbb{R}$, define the Orlicz class $L_{\\Phi_{i}}(\\mathbb{R_+})$ to be the set of Lebesgue-measurable functions $f$ on $\\mathbb{R_+}$ such that \\begin{equation*} \\int_{\\mathbb{R_+}} \\Phi_{i} \\left( k|(Tf)(t)| \\right) t^{\\gamma}dt < \\infty \\end{equation*} for some $k>0$.\n  Our goal in this paper is to find conditions on $\\Phi_1$, $\\Phi_2$, $\\gamma$ and an operator $T$ so that the assertions \\begin{equation} T : L_{\\Phi_2,t^{\\gamma}}(\\mathbb{R_+}) \\rightarrow L_{\\Phi_1,t^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01478","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"}