Sum of some product-type operators from mixed-norm spaces to weighted-type spaces on the unit ball

AIMS Mathematics

article

Cheng-shi Huang¹  Zhi-jie Jiang¹  Yan-fu Xue¹ 

[1] School of Mathematics and Statistics, Sichuan University of Science and Engineering;South Sichuan Center for Applied Mathematics, Sichuan University of Science and Engineering

关键词: product-type operator;    boundedness;    compactness;    mixed-norm space;    weighted-type space;    essential norm;    Hilbert-Schmidt norm;   

DOI  :  10.3934/math.20221001

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

Let $ u_{j} $ be the holomorphic functions on the open unit ball $ \mathbb{B} $ in $ \mathbb{C}^{n} $, $ j = \overline{0, m} $, $ \varphi $ a holomorphic self-map of $ \mathbb{B} $, and $ \Re^{j} $ the $ j $th iterated radial derivative operator. In this paper, the boundedness and compactness of the sum operator $ \mathfrak{S}^m_{\vec{u}, \varphi} = \sum_{j = 0}^m M_{u_j}C_\varphi\Re^j $ from the mixed-norm space $ H(p, q, \phi) $, where $ 0 < p, q < +\infty $, and $ \phi $ is normal, to the weighted-type space $ H^\infty_\mu $ are characterized. For the mixed-norm space $ H(p, q, \phi) $, $ 1\leq p < +\infty $, $ 1 < q < +\infty $, the essential norm estimate of the operator is given, and the Hilbert-Schmidt norm of the operator on the weighted Bergman space $ A^2_\alpha $ is also calculated.

【 授权许可】

CC BY