{"paper":{"title":"The John--Nirenberg constant of ${\\rm BMO}^p,$ $1\\le p\\le 2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Leonid Slavin","submitted_at":"2015-06-16T13:48:33Z","abstract_excerpt":"We compute the exact John--Nirenberg constant of ${\\rm BMO}^p((0,1))$ for $1\\le p\\le 2,$ which has been known only for $p=1$ and $p=2.$ We also show that this constant is attained in the weak-type John--Nirenberg inequality and obtain a sharp lower estimate for the distance in ${\\rm BMO}^p$ to $L^\\infty.$ These results rely on sharp $L^p$- and weak-type estimates for logarithms of $A_\\infty$ weights, which in turn use the exact expressions for the corresponding Bellman functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04969","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"}