{"paper":{"title":"Characterizations of $A_2$ Matrix Power Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Katherine Lunceford, Kelly Bickel, Naba Mukhtar","submitted_at":"2016-05-19T18:03:43Z","abstract_excerpt":"In the scalar setting, the power functions $|x|^{\\gamma}$, for $-1 < \\gamma<1$, are the canonical examples of $A_2$ weights. In this paper, we study two types of power functions in the matrix setting, with the goal of obtaining canonical examples of $A_2$ matrix weights. We first study Type 1 matrix power functions, which are $n\\times n$ matrix functions whose entries are of the form $a|x|^{\\gamma}.$ Our main result characterizes when these power functions are $A_2$ matrix weights and has two extensions to Type $1$ power functions of several variables. We also study Type 2 matrix power functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06071","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"}