Singular maximal functions and Radon transforms near L¹

2002/05/14 by Andreas Seeger, Terence Tao, Seeger, Andreas +3
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #math.CA

paper · pdf · doi:10.48550/arxiv.math/0205156

32 pages

arxiv created 2002/05/14 · openalex publication_date 2002/05/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that some singular maximal functions and singular Radon transforms satisfy a weak type Lloglog L inequality. Examples include the maximal function and Hilbert transform associated to averages along a parabola. The weak type inequality yields pointwise convergence results for functions which are locally in Lloglog L.

Citations

• Lacunary spherical means

Related

• The limiting weak type behaviors and The lower bound for a new weak Llog L type norm of strong maximal operators
• Multi-parameter singular Radon transforms II: the L^p theory
• Maximal Polynomial Modulations of Singular Radon Transforms
• Weak type bounds for rough maximal singular integrals near L¹
• On extremals for a Radon-like transform