{"paper":{"title":"On the Calder\\'{o}n-Zygmund structure of Petermichl's kernel. Weighted inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hugo Aimar, Ivana G\\'omez","submitted_at":"2017-09-13T22:02:30Z","abstract_excerpt":"We show that Petermichl's dyadic operator $\\mathcal{P}$ (S. Petermichl (2000), Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol) is a Calder\\'{o}n-Zygmund type operator on an adequate metric normal space of homogeneous type. As a consequence of a general result on spaces of homogeneous type, we get weighted boundedness of the maximal operator $\\mathcal{P}^*$ of truncations of the singular integral. We show that dyadic $A_p$ weights are the good weights for the maximal operator $\\mathcal{P}^*$ of the scale truncations of $\\mathcal{P}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04552","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"}