{"paper":{"title":"Anisotropic Ornstein non inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dmitriy M. Stolyarov, Krystian Kazaniecki, Michal Wojciechowski","submitted_at":"2015-05-20T15:19:47Z","abstract_excerpt":"We investigate existence of a priori estimates for differential operators in $L^1$ norm: for anisotropic homogeneous differential operators $T_1, \\ldots , T_{\\ell}$, we study the conditions under which the inequality $$ \\|T_1 f\\|_{L_1(\\mathbb{R}^d)} \\lesssim \\sum\\limits_{j = 2}^{\\ell}\\|T_j f\\|_{L_1(\\mathbb{R}^d)} $$ holds true. We also discuss a similar problem for martingale transforms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05416","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"}