LIPSCHITZ TYPE CHARACTERIZATIONS OF HARMONIC BERGMAN SPACES

Title & Authors
LIPSCHITZ TYPE CHARACTERIZATIONS OF HARMONIC BERGMAN SPACES
Nam, Kyesook;

Abstract
Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of $\small{C^n}$ 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 $\small{R^n}$. Furthermore, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < $\small{{\infty}}$. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.
Keywords
weighted harmonic Bergman spaces;unit ball;upper half-space;
Language
English
Cited by
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