AIMS Mathematics | |
Sum of some product-type operators from mixed-norm spaces to weighted-type spaces on the unit ball | |
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
【 预 览 】
Files | Size | Format | View |
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RO202302200002224ZK.pdf | 291KB | download |