Vector-valued operators, optimal weighted estimates and the C_p condition  

作　　者：María Eugenia Cejas Kangwei Li Carlos Pérez Israel Pablo Rivera-Ríos 

机构地区：[1]BCAM—Basque Center for Applied Mathematics,Bilbao 48009,Spain [2]CONICET,Departamento de Matematica,Facultad de Ciencias Exactas,Universidad Nacional de La Plata,La Plata 1900,Argentina [3]Department of Mathematics,University of the Basque Country,Bilbao 48080,Spain [4]Ikerbasque,Basque Foundation of Science,Bilbao 48013,Spain [5]INMABB,CONICET,Departamento de Matematica,Universidad Nacional del Sur,Bahia Blanca 8000,Argentina

出　　处：《Science China Mathematics》2020年第7期1339-1368,共30页中国科学：数学（英文版）

基　　金：supported by the Basque Government through the Basque Excellence Research Centre 2018–2021 Program;Agencia Estatal de Investigacion/European Regional Development Fund of UE(Grant No.MTM 2017-82160-C2-1-P),Acronym“Harmonic Analysis and Quantum Mechanics”;Spanish Ministry of Economy and Competitiveness through Basque Center for Applied Mathematics Severo Ochoa Excellence Accreditation(Grant No.SEV-2013-0323);Universidad Nacional del Sur(Grant No.11/X752);Agencia Nacional de Promocion Cientifica y Tecnologica of Argentina(Grant No.PICT 2014-1771);Juan de la Cierva-Formacion2015(Grant No.FJCI-2015-24547);Consejo Nacional de Investigaciones Cientificas y Tecnicas/Proyectos de Investigacion Plurianuales of Argentina(Grant No.11220130100329CO)。

摘　　要：In this paper some new results concerning the C_p classes introduced by Muckenhoupt(1981)and later extended by Sawyer(1983),are provided.In particular,we extend the result to the full expected range p>0,to the weak norm,to other operators and to their vector-valued extensions.Some of those results rely upon sparse domination,which in the vector-valued case are provided as well.We will also provide sharp weighted estimates for vector-valued extensions relying on those sparse domination results.

关 键 词：A_p weights quantitative estimates C_p estimates vector-valued extensions sparse domination maximal functions Calderon-Zygmund operators COMMUTATORS 

分 类 号：O177[理学—数学]