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Riemann-Stieltjes operators from https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq1_HTML.gif spaces to https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq2_HTML.gif -Bloch spaces on the unit ball

Journal of Inequalities and Applications20062006:27874

DOI: 10.1155/JIA/2006/27874

Received: 5 December 2005

Accepted: 19 April 2006

Published: 28 August 2006

Abstract

Let https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq3_HTML.gif denote the space of all holomorphic functions on the unit ball https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq4_HTML.gif . We investigate the following integral operators: https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq5_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq6_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq7_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq8_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq9_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq10_HTML.gif is the radial derivative of https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq11_HTML.gif . The operator https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq12_HTML.gif can be considered as an extension of the Cesàro operator on the unit disk. The boundedness of two classes of Riemann-Stieltjes operators from general function space https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq13_HTML.gif , which includes Hardy space, Bergman space, https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq14_HTML.gif space, BMOA space, and Bloch space, to https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq15_HTML.gif -Bloch space https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F27874/MediaObjects/13660_2005_Article_1580_IEq16_HTML.gif in the unit ball is discussed in this paper.

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Authors’ Affiliations

(1)
Department of Mathematics, JiaYing University
(2)
Department of Mathematics, Shantou University

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Copyright

© Li 2006

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