Forelli-Rudin type theorem in pluriharmonic Bergman spaces with small index |
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Authors: | Guangbin Ren Jihuai Shi |
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Institution: | (1) Department of Mathematics, University of Science and Technology of China, 230026 Hefei, China |
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Abstract: | It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL
p
(B)∩h(B) onto Bergman spaceL
p
(B) ∩
H(B) for 0p 1 ands (p1-1)(n+1). As an application it is shown that the Gleason’s problem can be solved in Bergman space LP(B)∩H(B) for 0p 1.
Project supported by the National Natural Science Foundation of China (Grant No. 19871081) and the Doctoral Program Foundation
of the State Education Commission of China. |
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Keywords: | Bergman operator Gleason problem pluriharmonic functions |
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