Area Operators on Bergman Spaces  

作　　者：Xiao Fen LV Jordi PAU Mao Fa WANG 

机构地区：[1]Department of Mathematics,Huzhou University,Huzhou 313000,P.R.China [2]Departament de Matemàtiques i Informàtica,Universitat de Barcelona,08007 Barcelona,Catalonia,Spain [3]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第5期1161-1176,共16页数学学报（英文版）

基　　金：partially supported by NSFC(Grant Nos.12171150,11771139);partially supported by NSFC(Grant Nos.12171373,12371136);ZJNSF(Grant No.LY20A010008);supported by the grants MTM2017-83499-P(Ministerio de Educación y Ciencia);2017SGR358(Generalitat de Catalunya)。

摘　　要：We completely characterize the boundedness of area operators from the Bergman spaces A_(α)^(p)(Bn)to the Lebesgue spaces L^(q)(S_(n))for all 0<p,q<∞.For the case n=1,some partial results were previously obtained by Wu in[Wu,Z.:Volterra operator,area integral and Carleson measures,Sci.China Math.,54,2487–2500(2011)].Especially,in the case q<p and q<s,we obtain some characterizations for the area operators to be bounded.We solve the cases left open there and extend the results to n-complex dimension.

关 键 词：Area operator Bergman space tent space area formula 

分 类 号：O177[理学—数学]