{"paper":{"title":"Weighted martingale multipliers in non-homogeneous setting and outer measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"A. Volberg, C. Thiele, S. Treil","submitted_at":"2014-11-19T20:13:48Z","abstract_excerpt":"We investigate the unconditional basis property of martingale differences in weighted $L^2$ spaces in the non-homogeneous situation (i.e. when the reference measure is not doubling).\n  Specifically, we prove that finiteness of the quantity $[w]_{A_2}=\\sup_I \\, < w>_I < w^{-1}>_I$, defined through averages $ <\\cdot >_I$ relative to the reference measure $\\nu$, implies that each martingale transform relative to $\\nu$ is bounded in $L^2(w\\, d\\nu)$. Moreover, we prove the linear in $[w]_{A_2}$ estimate of the unconditional basis constant of the Haar system.\n  Even in the classical case of the stan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5345","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"}