{"paper":{"title":"$p$-regularity and weights for operators between $L^p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrique A. S\\'anchez P\\'erez, Pedro Tradacete","submitted_at":"2018-03-28T14:39:49Z","abstract_excerpt":"We explore the connection between $p$-regular operators on Banach function spaces and weighted $p$-estimates. In particular, our results focus on the following problem. Given finite measure spaces $\\mu$ and $\\nu$, let $T$ be an operator defined from a Banach function space $X(\\nu)$ and taking values on $L^p (v d \\mu)$ for $v$ in certain family of weights $V\\subset L^1(\\mu)_+$: we analyze the existence of a bounded family of weights $W\\subset L^1(\\nu)_+$ such that for every $v\\in V$ there is $w \\in W$ in such a way that $T:L^p(w d \\nu) \\to L^p(v d \\mu)$ is continuous uniformly on $V$. A conditi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10652","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"}