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.
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.
引文
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