{"paper":{"title":"Lower bounds for the dyadic Hilbert transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Brett D. Wick, Elodie Pozzi (IMB), Philippe Jaming (IMB)","submitted_at":"2016-05-18T10:47:24Z","abstract_excerpt":"In this paper, we seek lower bounds of the dyadic Hilbert transform (Haar shift) of the form $\\left\\Vert S f\\right\\Vert_{L^2(K)}\\geq C(I,K)\\left\\Vert f\\right\\Vert_{L^2(I)}$ where $I$ and $K$ are two dyadic intervals and $f$ supported in $I$. If $I\\subset K$ such bound exist while in the other cases $K\\subsetneq I$ and $K\\cap I=\\emptyset$ such bounds are only available under additional constraints on the derivative of $f$. In the later case, we establish a bound of the form $\\left\\Vert S f\\right\\Vert_{L^2(K)}\\geq C(I,K)|\\left\\langle f\\right\\rangle_I|$ where $\\left\\langle f\\right\\rangle_I$ is th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05511","kind":"arxiv","version":4},"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"}