Revista Matemática Iberoamericana

Outer and inner vanishing measures and division in $H^\infty + C$

Keiji Izuchi

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Measures on the unit circle are well studied from the view of Fourier analysis. In this paper, we investigate measures from the view of Poisson integrals and of divisibility of singular inner functions in $H^\infty + C$. Especially, we study singular measures which have outer and inner vanishing measures. It is given two decompositions of a singular positive measure. As applications, it is studied division theorems in $H^\infty + C$.

Article information

Rev. Mat. Iberoamericana, Volume 18, Number 3 (2002), 511-540.

First available in Project Euclid: 28 April 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46J15: Banach algebras of differentiable or analytic functions, Hp-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]

Singular inner function bounded analytic function $H^\infty + C$


Izuchi, Keiji. Outer and inner vanishing measures and division in $H^\infty + C$. Rev. Mat. Iberoamericana 18 (2002), no. 3, 511--540.

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