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Boundedness of the Bergman type operators on mixed norm spaces

Author: Yongmin Liu
Journal: Proc. Amer. Math. Soc. 130 (2002), 2363-2367
MSC (2000): Primary 47B38; Secondary 32A30, 46E15
Published electronically: January 23, 2002
MathSciNet review: 1897461
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Abstract: Conditions sufficient for boundedness of the Bergman type operators on certain mixed norm spaces $L_{p,q}(\varphi) (0<p<1, 1<q<\infty)$ of functions on the unit ball of $C^n$ are given, and this is used to solve Gleason's problem for the mixed norm spaces $H_{p,q}(\varphi) (0<p<1,1<q<\infty)$.

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Additional Information

Yongmin Liu
Affiliation: Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, People’s Republic of China

Keywords: Bergman type operator, normal function, boundedness, H\"older inequality, Gleason's problem
Received by editor(s): November 14, 2000
Received by editor(s) in revised form: March 19, 2001
Published electronically: January 23, 2002
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society