Sharp logarithmic inequalities for Riesz transforms

DOI10.1016/j.jfa.2012.04.007zbMath1247.42016OpenAlexW2094347065MaRDI QIDQ435853

Adam Osȩkowski

Publication date: 12 July 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2012.04.007

zbMATH Keywords

Hilbert transformmartingalebest constantRiesz transformdifferential subordination\(L \log L\) inequalityre-expansion operator

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20)

Related Items (11)

Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups ⋮ A probabilistic approach to Hilbert transforms on free group von Neumann algebras ⋮ Survey article: Bellman function method and sharp inequalities for martingales ⋮ Inequalities for the truncated Hilbert transform and the segment multiplier ⋮ Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms ⋮ Distributions of anisotropic order and applications to H-distributions ⋮ Sharp weak type estimates for Riesz transforms ⋮ On a class of Calderón-Zygmund operators arising from projections of martingale transforms ⋮ On the action of Riesz transforms on the class of bounded functions ⋮ Sharp \(L^p\) bound for holomorphic functions on the unit disc ⋮ Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space

Cites Work

• Orthogonal martingales under differential subordination and applications to Riesz transforms
• 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
• Sharp inequalities for BMO functions
• 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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