Poly-Bergman Projections and Orthogonal Decompositions of L2-spaces Over Bounded Domains
Poly-Bergman Projections and Orthogonal Decompositions of L2-spaces Over Bounded Domains
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有界域上 L2 空间的 Poly-Bergman 投影和正交分解
DOI：
10.1007/978-3-7643-8684-9_12
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
L. V. Pessoa
中科院分区：
文献类型：
--
作者：
Y. Karlovich;L. V. Pessoa
利用单位圆盘D上的奇异积分算子SD和SD*，得到了单位圆盘上不同的真多Bergman投影和反多Bergman投影的显式表示，研究了单位圆盘上由算子SD和SD*实现的不同真多Bergman空间和真反多Bergman空间之间的关系，建立了任意有界开⊂ℂ的空间L2(U，da)(关于多Bergman空间和反Poly Bergman空间)的两种新的正交分解，并考虑了对Dzhuraev公式的违反，建立了几个开扇区的Bergman投影和反Bergman投影的显式.
The paper is devoted to obtaining explicit representations of poly-Bergman and anti-poly-Bergman projections in terms of the singular integral operatorsSDandSD*on the unit diskD, studying relations between different true poly-Bergman and true anti-poly-Bergman spaces on the unit disk that are realized by the operatorsSDandSD*, establishing two new orthogonal decompositions of the spaceL2(U, dA) (in terms of poly-Bergman and anti-poly-Bergman spaces) for an arbitrary bounded open setU⊂ ℂ with the Lebesgue area measuredA, considering violation of Dzhuraev’s formulas and establishing explicit forms of the Bergman and anti-Bergman projections for several open sectors.