{"paper":{"title":"$L^p$ boundedness of non-homogeneous Littlewood-Paley $g^*_{\\lambda,\\mu}$-function with non-doubling measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mingming Cao, Qingying Xue","submitted_at":"2016-05-16T05:24:28Z","abstract_excerpt":"It is well-known that the $L^p$ boundedness and weak $(1,1)$ estiamte $(\\lambda>2)$ of the classical Littlewood-Paley $g_{\\lambda}^{*}$-function was first studied by Stein, and the weak $(p,p)$ $(p>1)$ estimate was later given by Fefferman for $\\lambda=2/p$. In this paper, we investigated the $L^p(\\mu)$ boundedness of the non-homogeneous Littlewood-Paley $g_{\\lambda,\\mu}^{*}$-function with non-convolution type kernels and a power bounded measure $\\mu$: $$ g_{\\lambda,\\mu}^*(f)(x) = \\bigg(\\iint_{{\\mathbb R}^{n+1}_{+}} \\Big(\\frac{t}{t + |x - y|}\\Big)^{m \\lambda} |\\theta_t^\\mu f(y)|^2 \\frac{d\\mu(y"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04649","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"}