{"paper":{"title":"Boundedness for fractional Hardy-type operator on Herz-Morrey spaces with variable exponent","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jianglong Wu","submitted_at":"2014-04-06T23:21:18Z","abstract_excerpt":"In this paper, the fractional Hardy-type operator of variable order $\\beta(x)$ is shown to be bounded from the Herz-Morrey spaces $M\\dot{K}_{p_{_{1}},q_{_{1}}(\\cdot)}^{\\alpha,\\lambda}(\\mathbb{R}^{n})$ with variable exponent $q_{1}(x)$ into the weighted space $M\\dot{K}_{p_{_{2}},q_{_{2}}(\\cdot)}^{\\alpha,\\lambda}(\\mathbb{R}^{n},\\omega)$, where $\\omega=(1+|x|)^{-\\gamma(x)}$ with some $\\gamma(x)>0$ and $ 1/q_{_{1}}(x)-1/q_{_{2}}(x)=\\beta(x)/n$ when $q_{_{1}}(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_{_{1}}(x)$ satisfies the logarithmic continuity condition bot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1633","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"}