首页|SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES F(p,q,s)
SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES F(p,q,s)
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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 Ig 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 Jg,we show that,for 0＜α ≤ 1,Jg 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 Jg acting on F(p,p-2,s).
integration operatorclosed range propertystrict singularity
陈家乐
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School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,China
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