{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QWX3VVF2UJVPHHTCU7KX3PTNZY","short_pith_number":"pith:QWX3VVF2","schema_version":"1.0","canonical_sha256":"85afbad4baa26af39e62a7d57dbe6dce173096432b7ea60ab2461f129a16a109","source":{"kind":"arxiv","id":"1709.03123","version":1},"attestation_state":"computed","paper":{"title":"Weighted jump and variational inequalities for rough operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guixiang Hong, Honghai Liu, Yanping Chen, Yong Ding","submitted_at":"2017-09-10T16:26:10Z","abstract_excerpt":"In this paper, we systematically study weighted jump and variational inequalities for rough operators. More precisely, we show some weighted jump and variational inequalities for the families $\\mathcal T:=\\{T_\\varepsilon\\}_{\\varepsilon>0}$ of truncated singular integrals and $\\mathcal M_{\\Omega}:=\\{M_{\\Omega,t}\\}_{t>0}$ of averaging operators with rough kernels, which are defined respectively by $$ T_\\varepsilon f(x)=\\int_{|y|>\\varepsilon}\\frac{\\Omega(y')}{|y|^n}f(x-y)dy$$ and $$M_{\\Omega,t} f(x)=\\frac1{t^n}\\int_{|y|0}$ of truncated singular integrals and $\\mathcal M_{\\Omega}:=\\{M_{\\Omega,t}\\}_{t>0}$ of averaging operators with rough kernels, which are defined respectively by $$ T_\\varepsilon f(x)=\\int_{|y|>\\varepsilon}\\frac{\\Omega(y')}{|y|^n}f(x-y)dy$$ and $$M_{\\Omega,t} f(x)=\\frac1{t^n}\\int_{|y|