Open Access

On an integral operator on the unit ball in https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq1_HTML.gif

Journal of Inequalities and Applications20052005:434806

DOI: 10.1155/JIA.2005.81

Received: 23 December 2003

Published: 1 February 2005

Abstract

Let https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq2_HTML.gif denote the space of all holomorphic functions on the unit ball https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq3_HTML.gif . In this paper, we investigate the integral operator https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq4_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq5_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq6_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq7_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq8_HTML.gif is the radial derivative of https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq9_HTML.gif . The operator can be considered as an extension of the Cesàro operator on the unit disk. The boundedness of the operator on https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.81/MediaObjects/13660_2003_Article_1533_IEq10_HTML.gif -Bloch spaces is considered.

Authors’ Affiliations

(1)
Mathematical Institute of Serbian Academy of Sciences and Arts

Copyright

© Stević 2005