# LIPSCHITZ TYPE CHARACTERIZATIONS OF HARMONIC BERGMAN SPACES

• Received : 2012.09.05
• Published : 2013.07.31
• 39 5

#### Abstract

Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of $C^n$ in terms of Lipschitz type conditions in three different metrics. In this paper, we study characterizations of the harmonic Bergman space on the upper half-space in $R^n$. Furthermore, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < ${\infty}$. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.

#### Keywords

weighted harmonic Bergman spaces;unit ball;upper half-space

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#### Cited by

1. New Characterizations for the Weighted Fock Spaces pp.1661-8262, 2018, https://doi.org/10.1007/s11785-018-0850-1

#### Acknowledgement

Supported by : NRF