On the best constants in the weak type inequalities for re-expansion operator and Hilbert transform

DOI10.1090/S0002-9947-2012-05640-6zbMath1279.42009OpenAlexW2158454674MaRDI QIDQ2841355

Adam Osȩkowski

Publication date: 25 July 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2012-05640-6

zbMATH Keywords

Hilbert transformmartingalere-expansion operatorcosine and sine Fourier transform

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) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Martingales with continuous parameter (60G44)

Related Items (2)

Distribution of the logarithmic derivative of a rational function on the line ⋮ On the action of Riesz transforms on the class of bounded functions

Cites Work

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• Best constants for the Riesz projection
• Best weak-type \((p,p)\) constants, \(1\leq p \leq 2\), for orthogonal harmonic functions and martingales
• Differential subordination and strong differential subordination for continuous-time martingales and related sharp inequalities
• Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms
• A superharmonic proof of the M. Riesz conjugate function theorem
• Best constants for some operators associated with the Fourier and Hilbert transforms
• On the best values of the constants in the theorem of M. Riesz, Zygmund and Kolmogorov
• On the Weak Type (1, 1) Inequality for Conjugate Functions

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