{"paper":{"title":"$L^p$ bounds for singular integrals and maximal singular integrals with rough kernels","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Atanas Stefanov, Loukas Grafakos","submitted_at":"1997-10-05T00:00:00Z","abstract_excerpt":"Convolution type Calder\\'on-Zygmund singular integral operators with rough kernels $\\pv \\Om(x)/|x|^n$ are studied. A condition on $\\Om$ implying that the corresponding singular integrals and maximal singular integrals map $L^p \\to L^p$ for $1<p<\\nf$ is obtained. This condition is shown to be different from the condition $\\Om\\in H^1(\\sn)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9710205","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"}