On ideals generated by bounded analytic functions in the bidisc

Urban Cegrell

Displaying similar documents to “On ideals generated by bounded analytic functions in the bidisc”

A value-distribution criterion for the class $L \log L$ and some related questions

M. Essen, D. F. Shea, C. S. Stanton (1985)

Annales de l'institut Fourier

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We give a necessary and sufficient condition for an analytic function in $H^{1}$ to have real part in class $L$ $log L$ . This condition contains the classical one of Zygmund; other variants are also given.

Sharp $L \log^{α} L$ inequalities for conjugate functions

Matts Essén, Daniel F. Shea, Charles S. Stanton (2002)

Annales de l’institut Fourier

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We give a method for constructing functions $φ$ and $ψ$ for which $H (x, y) = φ (x) - ψ (y)$ has a specified subharmonic minorant $h (x, y)$ . By a theorem of B. Cole, this procedure establishes integral mean inequalities for conjugate functions. We apply this method to deduce sharp inequalities for conjugates of functions in the class $L {log}^{α} L$ , for $- 1 \leq α < \infty$ . In particular, the case $α = 1$ yields an improvement of Pichorides’ form of Zygmund’s classical inequality for the conjugates of functions in $L log L$ . We also apply the method to produce a new...

An explicit formula for the Mahler measure of a family of $3$ -variable polynomials

Chris J. Smyth (2002)

Journal de théorie des nombres de Bordeaux

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An explicit formula for the Mahler measure of the $3$ -variable Laurent polynomial $a + b x^{- 1} + c y + (a + b x + c y) z$ is given, in terms of dilogarithms and trilogarithms.

Multivalent functions and $Q_{K}$ spaces.

Wulan, Hasi (2004)

International Journal of Mathematics and Mathematical Sciences

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Some problems of analytic number theory

K. Ramachandra (1976)

Acta Arithmetica

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Some Estimates of the Integral $i n t_{0}^{2 p i} e x t L o g, | p (e^{i h e t a}) | {(2 p i)}^{- 1}, d h e t a$

Stojan Radenović (1992)

Publications de l'Institut Mathématique

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Absolute values of BMOA functions.

Konstantin M. Dyakonov (1999)

Revista Matemática Iberoamericana

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The paper contains a complete characterization of the moduli of BMOA functions. These are described explicitly by a certain Muckenhoupt-type condition involving Poisson integrals. As a consequence, it is shown that an outer function with BMO modulus need not belong to BMOA. Some related results are obtained for the Bloch space.

A simple elementary proof of $M (x) = \sum_{n \leq x} μ (n) = o (x)$

M. Kalecki (1967)

Acta Arithmetica

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