Dimension free estimates for discrete Riesz transforms on products of abelian groups

DOI10.1016/j.aim.2003.07.002zbMath1044.43001OpenAlexW2077247084MaRDI QIDQ596609

Françoise Lust-Piquard

Publication date: 10 August 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2003.07.002

zbMATH Keywords

discrete groupRiesz transform

Mathematics Subject Classification ID

Multipliers for harmonic analysis in several variables (42B15) Noncommutative dynamical systems (46L55) Dilations, extensions, compressions of linear operators (47A20) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (9)

Second order Riesz transforms on multiply-connected Lie groups and processes with jumps ⋮ Bellman functions and dimension free \(L^p\)-estimates for the Riesz transforms in Bessel settings ⋮ On some operators associated with non-degenerate symmetric \(\alpha \)-stable probability measures ⋮ Dimension free \(L^p\) estimates for single Riesz transforms via an \(H^\infty\) joint functional calculus ⋮ Sharp \(L^p\) estimates for discrete second-order Riesz transforms ⋮ On the \(\ell^p\)-norm of the discrete Hilbert transform ⋮ Sharp \(L^p\) estimates for discrete second order Riesz transforms ⋮ Discrete Hilbert transform à la Gundy–Varopoulos ⋮ Discrete harmonic analysis associated with ultraspherical expansions

Cites Work

• Gaussian estimates for Markov chains and random walks on groups
• Generalized analyticity in UMD spaces
• Non commutative Khintchine and Paley inequalities
• Markov chains, Riesz transforms and Lipschitz maps
• Riesz transforms associated with the number operator on the Walsh system and the fermions
• Non-commutative martingale inequalities
• Riesz transforms on deformed Fock spaces
• Abstract Spectral Decompositions Guaranteed by the Hilbert Transform
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
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