The Orthogonal Decomposition of L~2 (B_2, dμ_α(z)) and Hankel Type Operators

Jian Xun HE(1),Li Zhong PENG(2

Acta Mathematica Sinica, Chinese Series ›› 2000, Vol. 43 ›› Issue (4) : 665-672.

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PDF(469 KB)
Acta Mathematica Sinica, Chinese Series ›› 2000, Vol. 43 ›› Issue (4) : 665-672. DOI: 10.12386/A2000sxxb0086
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The Orthogonal Decomposition of L~2 (B_2, dμ_α(z)) and Hankel Type Operators

  • Jian Xun HE(1),Li Zhong PENG(2
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Abstract

Let B2 be the unit ball of 2-dimensional complex plane C2, dμα(z) = dm(z)(α>-1) the weighted measure. From the view point of the Cauchy-Riemann operator and the triangle polynomial given in [1], we obtain an or thogonal decomposition and orthogonal basis, where A0(+,+) and A0(-, -) are the Bergman and anti-Bergman spaces respectively. This decomposition can be extended to L2(Bn, dμα(z)). In addi tion, we also obtain some results for Hankel type operators.

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Jian Xun HE(1),Li Zhong PENG(2. The Orthogonal Decomposition of L~2 (B_2, dμ_α(z)) and Hankel Type Operators. Acta Mathematica Sinica, Chinese Series, 2000, 43(4): 665-672 https://doi.org/10.12386/A2000sxxb0086
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