Note on Characterizations of the Harmonic Bergman Space

Nam, Kyesook; Na, Kyunguk; Choi, Eun Sun

doi:10.1007/978-3-0348-0297-0_29

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Cited by 2 publications

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“…In addition, we prove the boundedness of a mapping defined by difference quotient of harmonic function for an application of our characterizations. In [11], it has been studied harmonic analogues in the setting of the unit ball, but with restriction 1 ≤ p < ∞. In Section 4, we extend characterizations to the full range 0 < p < ∞.…”

Section: Introductionmentioning

confidence: 99%

Lipschitz Type Characterizations of Harmonic Bergman Spaces

Nam¹

2013

Bulletin of the Korean Mathematical Society

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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 < ∞. 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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Section: Introductionmentioning

confidence: 99%