SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES F(p,q,s)  

作　　者：陈家乐 Jiale CHEN(School of Mathematics and Statistics,Shaanxi Normal University,Xi’an,710119,China)

机构地区：[1]School of Mathematics and Statistics,Shaanxi Normal University,Xi’an,710119,China

出　　处：《Acta Mathematica Scientia》2024年第1期173-188,共16页数学物理学报（B辑英文版）

基　　金：partially supported by the Fundamental Research Funds for the Central Universities(GK202207018)of China。

摘　　要：We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_(g)on F(p,pα-2,s),which generalizes the existing results and answers a question raised in[A.Anderson,Integral Equations Operator Theory,69(2011),no.1,87-99].For the Volterra operator J_(g),we show that,for 0<α≤1,J_(g)never has a closed range on F(p,pα-2,s).We then prove that the notions of compactness,weak compactness and strict singularity coincide in the case of J_(g)acting on F(p,p-2,s).

关 键 词：integration operator closed range property strict singularity 

分 类 号：O177[理学—数学]