Abstract
We obtain the explicit formulae for the harmonic Bergman kernels of B n \{0} and \(\mathbb{R}^n \backslash \overline {B_n } \) and study the connection between harmonic Bergman kernel and weighted harmonic Bergman kernel. We also get the explicit formula for the weighted harmonic Bergman kernel of B n \{0} with the weight \(\tfrac{1} {{|x|^4 }} \).
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Supported by National Natural Science Foundation of China (Grant No. 10401024)
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Zhao, Z.G. The harmonic Bergman kernels for punctured domains. Acta. Math. Sin.-English Ser. 30, 1977–1988 (2014). https://doi.org/10.1007/s10114-014-1623-z
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DOI: https://doi.org/10.1007/s10114-014-1623-z