Boundedness of the Bergman type operators on mixed norm spaces
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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 $H_{p,q}(\varphi )\ (0<p<1,1<q<\infty )$.References
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Additional Information
- Yongmin Liu
- Affiliation: Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, People’s Republic of China
- Email: minliu@263.net
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2363-2367
- MSC (2000): Primary 47B38; Secondary 32A30, 46E15
- DOI: https://doi.org/10.1090/S0002-9939-02-06332-3
- MathSciNet review: 1897461