Moment vanishing properties of harmonic Bergman functions |
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Authors: | Boo Rim Choe Heungsu Yi |
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Affiliation: | a Department of Mathematics, Korea University, Seoul 136-701, South Korea b Department of Mathematics, Research Institute of Basic Sciences, Kwangwoon University, Seoul 139-701, South Korea |
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Abstract: | We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces bδp on the upper half-space must have the moment vanishing properties. As an application, we show that b0p, p?1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to bδp. |
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Keywords: | Moment vanishing properties Weighted harmonic Bergman functions Half-space |
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