Volume 11, Issue 1 (4-2016)                   IJMSI 2016, 11(1): 27-34 | Back to browse issues page

‎ 10.7508/ijmsi.2016.01.003

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Double Integral Characterization for Bergman Spaces
M. Hassanlou , H. Vaezi
Abstract:  

‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be in Bergman spaces‎.

Keywords: Bergman spaces, Pseudo-hyperbolic metric, Hyperbolic metric, Double integral.
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Type of Study: Research paper | Subject: Special
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