Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛
We obtain weighted integral representations for spaces of functions holomorphic in the unit ball 𝐵𝑛 and belonging to area-integrable weighted 𝐿𝑝-classes with “anisotropic” weight function of the type ∏𝑛𝑖=1(1−|𝑤1|2−|𝑤2|2−⋯−|𝑤𝑖|2)𝛼𝑖, 𝑤=(𝑤1,𝑤2,…,𝑤𝑛)∈𝐵𝑛. The corresponding kernels of these representation...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/354961 |
| Summary: | We obtain weighted integral representations for spaces of functions holomorphic in the unit ball 𝐵𝑛 and belonging to area-integrable weighted 𝐿𝑝-classes with “anisotropic” weight function of the type ∏𝑛𝑖=1(1−|𝑤1|2−|𝑤2|2−⋯−|𝑤𝑖|2)𝛼𝑖, 𝑤=(𝑤1,𝑤2,…,𝑤𝑛)∈𝐵𝑛. The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for 𝑛=2). |
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| ISSN: | 1085-3375 1687-0409 |