{"paper":{"title":"Non-homogeneous $Tb$ Theorem for Bi-parameter $g$-Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Mingming Cao, Qingying Xue","submitted_at":"2016-04-24T14:50:11Z","abstract_excerpt":"The main result of this paper is a bi-parameter $Tb$ theorem for Littlewood-Paley $g$-function, where $b$ is a tensor product of two pseudo-accretive functions. Instead of the doubling measure, we work with a product measure $\\mu = \\mu_n \\times \\mu_m$, where the measures $\\mu_n$ and $\\mu_m$ are only assumed to be upper doubling. The main techniques of the proof include a bi-parameter $b$-adapted Haar function decomposition and an averaging identity over good double Whitney regions. Moreover, the non-homogeneous analysis and probabilistic methods are used again."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07037","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"}