Affiliation:
1. School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, P. R. China
2. South Sichuan Center for Applied Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, P. R. China
Abstract
<abstract><p>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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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