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Commun. Korean Math. Soc. 2006; 21(3): 419-428
Printed September 1, 2006
Copyright © The Korean Mathematical Society.
A BMO type characterization of weighted Lipschitz functions in terms of the Berezin transform
Hong Rae Cho, Yeoung-Tae Seo
Pusan National University, Pusan National University
The Berezin transform is the analogue of the Poisson transform in the Bergman spaces. Dyakonov characterize the holomorphic weighted Lipschitz function in the unit disk in terms of the Poisson integral. In this paper, we characterize the harmonic weighted Lipschitz function in terms of the Berezin transform instead of the Poisson integral.
Keywords: weighted Lipschitz space of harmonic functions, Berezin transform, a regular modulus of continuity
MSC numbers: 31A05, 31A10
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