Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs

DOI10.1112/plms/pdr061zbMath1271.42024arXiv1101.1734OpenAlexW2149986288MaRDI QIDQ2901906

Xavier Tolsa, Albert Mas

Publication date: 31 July 2012

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.1734

zbMATH Keywords

singular integralCauchy transformLipschitz graphsmooth truncation\(n\)-dimensional Riesz transform

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25)

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A noncommutative weak type \((1,1)\) estimate for a square function from ergodic theory ⋮ Regularity of \(\mathcal C^1\) and Lipschitz domains in terms of the Beurling transform ⋮ Smoothness of the Beurling transform in Lipschitz domains ⋮ Weighted variation inequalities for differential operators and singular integrals in higher dimensions ⋮ $L^p$ estimates for the variation for singular integrals on uniformly rectifiable sets ⋮ Weighted variational inequalities for singular integrals on spaces of homogeneous type ⋮ Weighted variation inequalities for differential operators and singular integrals ⋮ Variation for the Riesz transform and uniform rectifiability ⋮ Vector valued \(q\)-variation for differential operators and semigroups. I ⋮ Vector valued \(q\)-variation for ergodic averages and analytic semigroups ⋮ Dimension-free estimates for the vector-valued variational operators ⋮ Variation and oscillation for harmonic operators in the inverse Gaussian setting ⋮ Variation for singular integrals on Lipschitz graphs: 𝐿^{𝑝} and endpoint estimates

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