{"paper":{"title":"Weighted norm inequalities for Calderon-Zygmund operators without doubling conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Xavier Tolsa","submitted_at":"2001-01-23T17:00:05Z","abstract_excerpt":"In this paper we develop a kind of A_p theory for Calderon-Zygmund operators in a non-homogeneous setting. Let \\mu be a Borel measure on \\R^d which may be non doubling. The only condition that \\mu must satisfy is \\mu(B(x,r))\\leq Cr^n for all x\\in\\R^d, r>0 and for some fixed n with 0<n\\leq d. We introduce a maximal operator N, which coincides with the maximal Hardy-Littlewood operator if \\mu(B(x,r))\\approx r^n for x\\in\\supp(\\mu), and we show that all n-dimensional Calderon-Zygmund operators are bounded on L^p(w d\\mu) if and only if N is bounded on L^p(w d\\mu), for a fixed p\\in(1,\\infty). Also, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101192","kind":"arxiv","version":2},"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"}