Bulletin of the Korean Mathematical Society (대한수학회보)

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LIPSCHITZ TYPE CHARACTERIZATIONS OF HARMONIC BERGMAN SPACES

  • Nam, Kyesook (Department of Mathematical Sciences BK21-Mathematical Sciences Division Seoul National University)
  • Received : 2012.09.05
  • Published : 2013.07.31
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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.

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References

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