Singular integrals along 𝑁 directions in ℝ²

DOI10.1090/S0002-9939-2010-10442-2zbMath1206.42009arXiv1001.1998OpenAlexW2764949456MaRDI QIDQ3065723

Ciprian Demeter

Publication date: 6 January 2011

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

Full work available at URL: https://arxiv.org/abs/1001.1998

zbMATH Keywords

Kakeya maximal functionmaximal singular operators

Mathematics Subject Classification ID

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

Related Items (16)

A sharp estimate for the Hilbert transform along finite order lacunary sets of directions ⋮ An analogy of the Carleson-Hunt theorem with respect to Vilenkin systems ⋮ \(L^2\) bounds for a maximal directional Hilbert transform ⋮ Square functions for bi-Lipschitz maps and directional operators ⋮ A maximal function for families of Hilbert transforms Along homogeneous curves ⋮ Almost everywhere convergence of \(T\) means with respect to the Vilenkin system of integrable functions ⋮ Directional square functions ⋮ Logarithmic \(L^p\) bounds for maximal directional singular integrals in the plane ⋮ Singular integrals along lacunary directions in \(\mathbb{R}^n\) ⋮ Directional maximal function along the primes ⋮ On Weyl multipliers of the rearranged trigonometric system ⋮ Almost-orthogonality principles for certain directional maximal functions ⋮ On logarithmic bounds of maximal sparse operators ⋮ A guide to Carleson's theorem ⋮ Maximal subspace averages ⋮ Maximal directional operators along algebraic varieties

Cites Work

• Some weighted norm inequalities concerning the Schrödinger operators
• Maximal operators over arbitrary sets of directions
• On maximal functions for Mikhlin-Hörmander multipliers
• On convergence and growth of partial sums of Fourier series
• On a conjecture of E. M. Stein on the Hilbert transform on vector fields
• Differentiation in lacunary directions
• Remarks on Maximal Operators Over Arbitrary Sets of Directions
• On unboundedness of maximal operators for directional Hilbert transforms
• Maximal theorems for the directional Hilbert transform on the plane
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