Volterra integral operator and essential norm on Dirichlet type spaces

Liu Yang; Ruishen Qian; Liu Yang; Ruishen Qian

doi:10.3934/math.2021586

AIMS Mathematics

2021, Volume 6, Issue 9: 10092-10104. doi: 10.3934/math.2021586

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Research article

Volterra integral operator and essential norm on Dirichlet type spaces

Liu Yang ¹,
Ruishen Qian ^{2
,
,}

1.
Department of Mathematics, Shanxi Xueqian Normal University, Xian 710100, shanxi, China
2.
School of Mathematics and Statistics, Lingnan Normal University, 524048, Zhanjiang, Guangdong, China

Received: 22 April 2021 Accepted: 06 July 2021 Published: 07 July 2021
MSC : 30D45, 30D50

In this paper, we study the boundedness and essential norm of Volterra integral operator $ V_g $ and integral operator $ S_g $ on Dirichlet type spaces $ {\mathcal{D}_{K, \alpha}} $.
- Volterra type operator,
- Dirichlet type spaces,
- essential norm
Citation: Liu Yang, Ruishen Qian. Volterra integral operator and essential norm on Dirichlet type spaces[J]. AIMS Mathematics, 2021, 6(9): 10092-10104. doi: 10.3934/math.2021586

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Abstract

In this paper, we study the boundedness and essential norm of Volterra integral operator $ V_g $ and integral operator $ S_g $ on Dirichlet type spaces $ {\mathcal{D}_{K, \alpha}} $.

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