On inverses of discrete rough Hilbert transforms

DOI10.4064/cm7551-2-2020zbMath1467.42029arXiv2007.14360OpenAlexW3095956038MaRDI QIDQ4997542

Maciej Paluszyński, Jacek Zienkiewicz

Publication date: 29 June 2021

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.14360

zbMATH Keywords

Hilbert transformsingular integral operators

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Density, gaps, topology (11B05)

Related Items (1)

On maximal function of discrete rough truncated Hilbert transforms

Cites Work

• Universally \(L^1\)-bad arithmetic sequences
• Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
• Divergent square averages
• Weak type (1,1) bounds for rough operators
• Discrete analogues in harmonic analysis: spherical averages
• Weak type \((1,1)\) estimates for a class of discrete rough maximal functions
• $L^p$ boundedness of discrete singular Radon transforms
• Waek type (1,1) estimates for inverses of discrete rough singular integral operators

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