{"paper":{"title":"Sharp bounds for $t$-Haar multipliers on $L^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jean Carlo Moraes, Maria Cristina Pereyra, Oleksandra Beznosova","submitted_at":"2012-12-16T03:54:03Z","abstract_excerpt":"We show that if a weight $w\\in C^d_{2t}$ and there is $q >1$ such that $w^{2t}\\in A_q^d$, then the $L^2$-norm of the $t$-Haar multiplier of complexity $(m,n)$ associated to $w$ depends on the square root of the $C^d_{2t}$-characteristic of $w$ times the square root $A^d_q$-characteristic of $w^{2t}$ % raised to the power $(p-1)/2$ times a constant that depends polynomially on the complexity. In particular, if $w\\in C^d_{2t}\\cap A_{\\infty}^d$ then $w^{2t}\\in A_q^d$ for some $q>1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3749","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"}