Translator Disclaimer
2021 Generalized Integration Operators from Weak to Strong Spaces of Vector-valued Analytic Functions
Jiale Chen, Maofa Wang
Taiwanese J. Math. Advance Publication 1-18 (2021). DOI: 10.11650/tjm/201208

Abstract

For a fixed nonnegative integer $m$, an analytic map $\varphi$ and an analytic function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued analytic function $f$, where $X$ is a Banach space. Some estimates for the norm of the operator $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtained. In particular, it is shown that the Volterra operator $J_b \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ is bounded if and only if $J_b \colon A^2_{\alpha} \to A^2_{\alpha}$ is in the Schatten class $S_p(A^2_{\alpha})$ for $2 \leq p \lt \infty$ and $\alpha \gt -1$. Some corresponding results are established for $X$-valued Hardy spaces and $X$-valued Fock spaces.

Citation

Download Citation

Jiale Chen. Maofa Wang. "Generalized Integration Operators from Weak to Strong Spaces of Vector-valued Analytic Functions." Taiwanese J. Math. Advance Publication 1 - 18, 2021. https://doi.org/10.11650/tjm/201208

Information

Published: 2021
First available in Project Euclid: 30 December 2020

Digital Object Identifier: 10.11650/tjm/201208

Subjects:
Primary: 47B38
Secondary: 46E40

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
18 PAGES


SHARE
Advance Publication
Back to Top