Embedding of Qp spaces into tent spaces and Volterra integral operator

Ruishen Qian; Xiangling Zhu; Ruishen Qian; Xiangling Zhu

doi:10.3934/math.2021042

AIMS Mathematics

2021, Volume 6, Issue 1: 698-711. doi: 10.3934/math.2021042

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Research article

Embedding of Q_p spaces into tent spaces and Volterra integral operator

Ruishen Qian ¹,
Xiangling Zhu ^{2
,
,}

1.
School of Mathematics and Statistics, Lingnan Normal University, 524048, Zhanjiang, Guangdong, P. R. China
2.
University of Electronic Science and Technology of China, Zhongshan Institute, 528402, Zhongshan, Guangdong, P. R. China

Received: 10 July 2020 Accepted: 22 October 2020 Published: 28 October 2020
MSC : 30H25, 47B38

In this paper, the boundedness and compactness of the inclusion mapping from $Q_p$ spaces into tent spaces $\mathcal{T}_{\frac{qp}{2}, s}^{q}$ are completely characterized when $q>2$. As an application, the boundedness of the Volterra integral operator $T_g$ from $Q_p$ to the space $\mathcal{LF}(q, q-2, \frac{qp}{2})$ is obtained. Moreover, the essential norm and compactness of $T_g$ are also investigated.
- Q_p space,
- tent space,
- Carleson measure,
- Volterra integral operator
Citation: Ruishen Qian, Xiangling Zhu. Embedding of Qp spaces into tent spaces and Volterra integral operator[J]. AIMS Mathematics, 2021, 6(1): 698-711. doi: 10.3934/math.2021042

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Abstract

In this paper, the boundedness and compactness of the inclusion mapping from $Q_p$ spaces into tent spaces $\mathcal{T}_{\frac{qp}{2}, s}^{q}$ are completely characterized when $q>2$. As an application, the boundedness of the Volterra integral operator $T_g$ from $Q_p$ to the space $\mathcal{LF}(q, q-2, \frac{qp}{2})$ is obtained. Moreover, the essential norm and compactness of $T_g$ are also investigated.

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