Lipschitz type characterizations of harmonic Bergman spaces
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Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of Cn in terms of Lipschitz type condi- tions in three different metrics. In this paper, we study characterizations of the harmonic Bergman space on the upper half-space in Rn. Further- more, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < 1. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.
Abstract
Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of Cn in terms of Lipschitz type condi- tions in three different metrics. In this paper, we study characterizations of the harmonic Bergman space on the upper half-space in Rn. Further- more, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < 1. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.
참고문헌 (16)
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