SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES ${F(p,q,s)}$*

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doi:10.1007/s10473-024-0109-z

Abstract: We study the closed range property and the strict singularity of integration operators acting on the spaces $F(p,p\alpha-2,s)$ . We completely characterize the closed range property of the Volterra companion operator $I_g$ on $F(p,p\alpha-2,s)$ , 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 $0<\alpha\leq1$ , $J_g$ never has a closed range on $F(p,p\alpha-2,s)$ . We then prove that the notions of compactness, weak compactness and strict singularity coincide in the case of $J_g$ acting on $F(p,p-2,s)$ .

Key words: integration operator, closed range property, strict singularity

CLC Number:

47G10

Jiale Chen. SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES ${F(p,q,s)}$ ^*[J].Acta mathematica scientia,Series B, 2024, 44(1): 173-188.

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