{"paper":{"title":"Weighted vector-valued estimates for a non-standard Calder\\'on-Zygmund operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guoen Hu","submitted_at":"2016-02-25T07:36:24Z","abstract_excerpt":"In this paper, the author considers the weighted vector-valued estimate for the operator defined by $$T_Af(x)={\\rm p.\\,v.}\\int_{\\mathbb{R}^n}\\frac{\\Omega(x-y)}{|x-y|^{n+1}}\\big(A(x)-A(y)-\\nabla A(y)\\big)f(y){\\rm d}y,$$ and the corresponding maximal operator $T_A^*$, where $\\Omega$ is homogeneous of degree zero, has vanishing moment of order one, $A$ is a function in $\\mathbb{R}^n$ such that $\\nabla A\\in {\\rm BMO}(\\mathbb{R}^n)$. By a pointwise estimate for $\\|\\{T_Af_k(x)\\}\\|_{l^q}$ and the weighted $L^p$ estimates for the sparse operator $$\\mathcal{A}_{\\mathcal{S},\\,L(\\log L)^\\beta}f(x)=\\sum_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07830","kind":"arxiv","version":3},"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"}