Multipliers for logarithmic Cauchy integrals in the ball |
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Authors: | E S Dubtsov |
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Institution: | (1) Lyman Briggs College, Michigan State University, East Lansing, MI 48825, USA |
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Abstract: | Let B
n
denote the unit ball in
\mathbbC \mathbb{C}
n
, n ≥ 1. Let K \mathcal{K}
0(n) denote the class of functions defined for z ∈ B
n
as a constant plus the integral of the kernel log(1/(1 −〈z, ζ〉)) against a complex Borel measure on the sphere {ζ ∈
\mathbbC \mathbb{C}
n
,: |ζ| = 1}. Properties of holomorphic functions g such that fg ∈ K \mathcal{K}
0(n) for all f ∈ K \mathcal{K}
0(n) are studied. The extended Cesàro operators are investigated on the spaces K \mathcal{K}
0(n), n ≥ 1. Bibliography: 15 titles. |
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Keywords: | |
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