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Journal of Function Spaces and Applications
Volume 7 (2009), Issue 3, Pages 209-223

Extended Cesáro operators between generalized Besov spaces and Bloch type spaces in the unit ball

Department of Mathematics, Tianjin University, Tianjin 300072, China

Received 1 September 2009

Academic Editor: Hans G. Feichtinger

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let 𝑔 be a holomorphic of the unit ball B in the n-dimensional complex space, and denote by Tg the extended Cesáro operator with symbol g. Let 0 < p < +∞, −n − 1 < q < +∞, q > −1 and α > 0, starting with a brief introduction to well known results about Cesáro operator, we investigate the boundedness and compactness of Tg between generalized Besov space B(p, q) and 𝛼α- Bloch space α in the unit ball, and also present some necessary and sufficient conditions.