On singular integral and martingale transforms

DOI10.1090/S0002-9947-09-04953-8zbMath1196.60078arXivmath/0701516OpenAlexW1982853844WikidataQ109553789 ScholiaQ109553789MaRDI QIDQ5189142

Stephen J. Montgomery-Smith, Eero Saksman, Stefan Geiss

Publication date: 8 March 2010

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

Full work available at URL: https://arxiv.org/abs/math/0701516

zbMATH Keywords

singular integralsUMD propertymartingale transforms

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Multipliers for harmonic analysis in several variables (42B15) Geometry and structure of normed linear spaces (46B20) Probabilistic methods in Banach space theory (46B09) Martingales and classical analysis (60G46)

Related Items (42)

Bounds for partial derivatives: necessity of UMD and sharp constants ⋮ The Hilbert Transform and Orthogonal Martingales in Banach Spaces ⋮ Second order Riesz transforms on multiply-connected Lie groups and processes with jumps ⋮ Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups ⋮ The dyadic representation theorem using smooth wavelets with compact support ⋮ A sharp maximal inequality for continuous martingales and their differential subordinates ⋮ A weak type $(1,1)$ estimate for the Hilbert operator in higher-dimensional setting ⋮ Fourier multipliers and weak differential subordination of martingales in UMD Banach spaces ⋮ A ratio inequality for nonnegative martingales and their differential subordinates ⋮ The foundational inequalities of D. L. Burkholder and some of their ramifications ⋮ Martingale decompositions and weak differential subordination in UMD Banach spaces ⋮ Elliptic problems and holomorphic functions in Banach spaces ⋮ Multilinear operator-valued Calderón-Zygmund theory ⋮ Sharp \(L^p\)-bounds for a perturbation of Burkholders martingale transform ⋮ Weak \(\Phi\)-inequalities for the Haar system and differentially subordinated martingales ⋮ Perturbation of Burkholder's martingale transform and Monge-Ampère equation ⋮ Subordination by conformal martingales in \(L^{p}\) and zeros of Laguerre polynomials ⋮ Martingale transforms and their projection operators on manifolds ⋮ Multilinear singular integrals on non-commutative \(L^p\) spaces ⋮ Local characteristics and tangency of vector-valued martingales ⋮ New Bellman Functions and Subordination by Orthogonal Martingales in L p , 1 < p ≤ 2 ⋮ Various Sharp Estimates for Semi-discrete Riesz Transforms of the Second Order ⋮ Logarithmic inequalities for Fourier multipliers ⋮ Sharp inequalities for the Haar system and Fourier multipliers ⋮ Maximal inequalities for martingales and their differential subordinates ⋮ The best constants for operator Lipschitz functions on Schatten classes ⋮ An operator-valued \(T(1)\) theorem for symmetric singular integrals in UMD spaces ⋮ Multiplier theorems via martingale transforms ⋮ Sharp weak-type inequalities for Fourier multipliers and second-order Riesz transforms ⋮ Sharp \(L^p\) estimates for discrete second order Riesz transforms ⋮ Linear bounds for Calderón-Zygmund operators with even kernel on UMD spaces ⋮ On a class of Calderón-Zygmund operators arising from projections of martingale transforms ⋮ Burkholder-Davis-Gundy inequalities in UMD Banach spaces ⋮ Some remarks on the \(L^p\) estimates for powers of the Ahlfors-Beurling operator ⋮ Even Fourier multipliers and martingale transforms in infinite dimensions ⋮ Stability in Burkholder's differentially subordinate martingales inequalities and applications to Fourier multipliers ⋮ On Astala's theorem for martingales and Fourier multipliers ⋮ Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space ⋮ Sharp maximal \(L^p\)-bounds for continuous martingales and their differential subordinates ⋮ Continuity of weighted estimates in $A_{p}$ norm ⋮ On strongly orthogonal martingales in UMD Banach spaces ⋮ Burkholder integrals, Morrey’s problem and quasiconformal mappings

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