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| 摘要: |
| 本文研究了上半空间和单位球上的调和Bergman-Orlicz空间的刻画及调和函数差商的有界性.给出了调和Bergman-Orlicz空间分别在欧氏度量，双曲型度量，伪双曲型度量下的Lipschitz型刻画.利用这些刻画获得了调和函数差商的有界性，这些结果推广了相应于上半空间和单位球上的调和Bergman空间上的结果. |
| 关键词: 调和Bergman-Orlicz空间 Lipschitz型刻画 双曲型度量 伪双曲型度量 |
| DOI： |
| 分类号:O174.3 |
| 基金项目:海南省自然科学基金（2018CXTD338）；国家自然科学基金（11761026；11761027）. |
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| LIPSCHITZ TYPE CHARACTERIZATIONS OF HARMONIC BERGMAN-ORLICZ SPACES |
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MA Ru-meng,XU Jing-shi
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| Abstract: |
| We study characterizations of harmonic Bergman-Orlicz spaces and the boundedness of difference quotients of harmonic functions on the upper half-space or the unit ball. First, we give Lipschitz type characterizations of harmonic Bergman-Orlicz spaces via the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. By these characterizations, we obtain the boundedness of difference quotients of harmonic functions on the upper half-space or the unit ball, which generalize those for harmonic Bergman spaces on the upper half-space or the unit ball. |
| Key words: harmonic Bergman-Orlicz space Lipschitz characterization hyperbolic metric pseudo hyperbolic metric |
