Best constants for some operators associated with the Fourier and Hilbert transforms

DOI10.4064/sm157-3-2zbMath1016.42006OpenAlexW2048412295MaRDI QIDQ4484599

Igor E. Verbitsky, Brian Hollenbeck, Nigel J. Kalton

Publication date: 12 June 2003

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/sm157-3-2

zbMATH Keywords

Hilbert transformoperator normre-expansion operatoridentity operatorcosine and sine Fourier transformsubharmonic minorantsplurisubharmonic minorants

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

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The Hilbert Transform and Orthogonal Martingales in Banach Spaces ⋮ Obituary: Nigel John Kalton, 1946-2010 ⋮ The ℓp$\ell ^p$ norm of the Riesz–Titchmarsh transform for even integer p$p$ ⋮ Hollenbeck-Verbitsky conjecture on best constant inequalities for analytic and co-analytic projections ⋮ Sharp logarithmic inequalities for Riesz transforms ⋮ On the action of the Hilbert transform on \(\ell_1^N\)-valued functions ⋮ On the norm of the operator $aI+bH$ on $L^p(\mathbb R)$ ⋮ Integral operators on Sobolev-Lebesgue spaces ⋮ On the action of Riesz transforms on the class of bounded functions ⋮ On Riesz type inequalities for harmonic mappings on the unit disk ⋮ On the best constants in the weak type inequalities for re-expansion operator and Hilbert transform ⋮ On strongly orthogonal martingales in UMD Banach spaces

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