On an integral operator on the unit ball in <inline-formula><graphic file="1029-242X-2005-434806-i1.gif"/></inline-formula>

• Main Author: Stevi&#263; Stevo
• Format: Article
• Language: English
• Published: SpringerOpen 2005-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2005/434806

<p/> <p>Let <inline-formula><graphic file="1029-242X-2005-434806-i2.gif"/></inline-formula> denote the space of all holomorphic functions on the unit ball <inline-formula><graphic file="1029-242X-2005-434806-i3.gif"/></inline-formula>. In this paper, we investigate the integral operator <inline-formula><graphic file="1029-242X-2005-434806-i4.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2005-434806-i5.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2005-434806-i6.gif"/></inline-formula>, where <inline-formula><graphic file="1029-242X-2005-434806-i7.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2005-434806-i8.gif"/></inline-formula> is the radial derivative of <inline-formula><graphic file="1029-242X-2005-434806-i9.gif"/></inline-formula>. The operator can be considered as an extension of the Ces&#224;ro operator on the unit disk. The boundedness of the operator on <inline-formula><graphic file="1029-242X-2005-434806-i10.gif"/></inline-formula>-Bloch spaces is considered.</p>