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

doi:10.1007/s10473-024-0109-z

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (1): 173-188.doi: 10.1007/s10473-024-0109-z

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

Jiale Chen

School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China

收稿日期:2022-10-08 修回日期:2023-07-13 出版日期:2024-02-25 发布日期:2024-02-27
作者简介:Jiale Chen, E-mail: jialechen@snnu.edu.cn
基金资助:
Fundamental Research Funds for the Central Universities (GK202207018) of China.

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

Jiale Chen

School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China

Received:2022-10-08 Revised:2023-07-13 Online:2024-02-25 Published:2024-02-27
About author:Jiale Chen, E-mail: jialechen@snnu.edu.cn
Supported by:
Fundamental Research Funds for the Central Universities (GK202207018) of China.

摘要/Abstract

摘要： 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 $F(p,p-2,s)$.

关键词: integration operator, closed range property, strict singularity

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

中图分类号:

47G10

Jiale Chen. SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES ${F(p,q,s)}$^*[J]. 数学物理学报(英文版), 2024, 44(1): 173-188.

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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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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