HILBERT TRANSFORMS ALONG LIPSCHITZ DIRECTION FIELDS: A LACUNARY MODEL

DOI10.1112/S0025579316000280zbMath1380.42012arXiv1606.08976MaRDI QIDQ5361208

Christoph Thiele, Shaoming Guo, Konstantin Tikhomirov

Publication date: 27 September 2017

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.08976

zbMATH Keywords

Lipschitz conditiondirectional Hilbert transformlacunary conditionHadwiger-Gohberg-Markus illumination conjecture

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Improved bounds for Hadwiger's covering problem via thin-shell estimates ⋮ A sharp estimate for the Hilbert transform along finite order lacunary sets of directions ⋮ Covering the boundary of a convex body with its smaller homothetic copies ⋮ Square functions for bi-Lipschitz maps and directional operators ⋮ Borsuk's problem, Boltyanski's illumination problem, and circumradius ⋮ Lipschitz linearization of the maximal hyperbolic cross multiplier ⋮ Singular integrals along lacunary directions in \(\mathbb{R}^n\) ⋮ Cube is a strict local maximizer for the illumination number ⋮ On the illumination of centrally symmetric cap bodies in small dimensions ⋮ Illuminating spiky balls and cap bodies ⋮ Covering by homothets and illuminating convex bodies

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