Integral operators mapping into the space of bounded analytic functions

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• 作者：Manuel D. Contreras^a ; ^{contreras@us.es" class="auth_mail" title="E-mail the corresponding author} ; José ; A. Pelá ; ez^b ; ^{japelaez@uma.es" class="auth_mail" title="E-mail the corresponding author} ; Christian Pommerenke^c ; ^{pommeren@math.tu-berlin.de" class="auth_mail" title="E-mail the corresponding author} ; Jouni Rä ; ttyä ; ^d ; ^{jouni.rattya@uef.fi" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Integral operators ; Space of bounded analytic functions
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：271
• 期：10
• 页码：2899-2943
• 全文大小：679 K

文摘

We address the problem of studying the boundedness, compactness and weak compactness of the integral operators $T_g(f)(z)={\int }_0^{z}f(\zeta )g^{\prime }(\zeta )d\zeta$ acting from a Banach space X   into bdec9e524fe777c4289a9f" title="Click to view the MathML source">H^∞$H^{\infty }$. We obtain a collection of general results which are appropriately applied and mixed with specific techniques in order to solve the posed questions to particular choices of X.