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

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

Annales de l’institut Fourier

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 proof of the...

Singularity of parabolic measures

Robert Kaufman, Jang-Mei Wu (1980)

Compositio Mathematica

Slowly growing subharmonic function II.

Matts Essén (1980)

Commentarii mathematici Helvetici

Small values of polynomials: Cartan, Pólya and others.

Lubinsky, D.S. (1997)

Journal of Inequalities and Applications [electronic only]

Smoothness of the Green function for a special domain

Serkan Celik, Alexander Goncharov (2012)

Annales Polonici Mathematici

We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions $g_{ℂ ∖ K}$ is estimated. Markov’s constants of the corresponding set are evaluated.

Displaying 1 – 9 of 9

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

Singularity of parabolic measures

Slowly growing subharmonic function II.

Small values of polynomials: Cartan, Pólya and others.

Smoothness of the Green function for a special domain

Some applications of generalized condensers in the theory of analytic functions.

Some properties of weighted hyperbolic polynomials.

Superharmonic functions and bounded point evaluations.

Sur le principe classique du maximum

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