{"paper":{"title":"An observation: cut-off of the weight $w$ does not increase the $A_{p_{1}, p_{2}}$-\"norm'' of $w$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Reznikov, Alexander Volberg, Vasiliy Vasyunin","submitted_at":"2010-08-21T14:18:30Z","abstract_excerpt":"We consider weights $w$ and their cut-offs: $w_a(t)=w(t)$ if $w(t)\\le a$ and $w_a(t)=a$ if $w(t)> a$. We consider a generalized $A_p$-``norm'' and prove that the ``norm'' of $w_a$ is not greater then the ``norm'' of $w$. Our proof in the case $w\\in A_2$ is especially simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3635","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"}