{"paper":{"title":"Garsia-Rodemich Spaces: Bourgain-Brezis-Mironescu space, embeddings and rearrangement invariant spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mario Milman","submitted_at":"2016-08-28T20:09:02Z","abstract_excerpt":"We extend the construction of Garsia-Rodemich spaces in different directions. We show that the new space \\textbf{B,} introduced by Bourgain-Brezis-Mironescu \\cite{bbm}, can be described via a suitable scaling of the Garsia-Rodemich norms. As an application we give a new proof of the embeddings $BMO\\subset$ \\textbf{B }$\\subset$ $L(n^{\\prime},\\infty).$ We then generalize the Garsia-Rodemich construction and introduce the $GaRo_{X}$ spaces associated with a rearrangement invariant space $X,$ in such a way that $GaRo_{X}=X,$ for a large class of rearrangement invariant spaces. The underlying inequ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07849","kind":"arxiv","version":4},"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"}