{"paper":{"title":"Weighted inequalities of Fefferman-Stein type for Riesz-Schr\\\"odinger Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bruno Bongioanni, Eleonor Harboure, Pablo Quijano","submitted_at":"2018-10-26T13:55:58Z","abstract_excerpt":"In this work we are concerned with Fefferman-Stein type inequalities. More precisely, given an operator $T$ and some $p$, $1<p<\\infty$, we look for operators $\\mathcal{M}$ such that the inequality $$\\int |Tf|^pw\\leq C\\int |f|^p \\mathcal{M}w$$ holds true for any weight $w$. Specifically, we are interested in the case of $T$ being any first or second order Riesz transform associated to the Schr\\\"odinger operator $L=-\\Delta + V$, with $V$ a non-negative function satisfying an appropriate reverse-H\\\"older condition. For the Riesz-Schr\\\"odinger transforms $\\nabla L^{-1/2}$ and $\\nabla^2 L^{-1}$ we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11331","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"}