On continuum incidence problems related to harmonic analysis.

DOI10.1016/S0022-1236(03)00081-8zbMath1043.42010arXivmath/0203291OpenAlexW2070357196MaRDI QIDQ1402322

Wilhelm Schlag

Publication date: 20 August 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0203291

zbMATH Keywords

averaging operatorscombinatorial methods

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (10)

Dimension estimates on circular (s,t)-Furstenberg sets ⋮ Polynomial effective equidistribution ⋮ Finitary analysis in homogeneous spaces ⋮ Polynomial effective density in quotients of \(\mathbb{H}^3\) and \(\mathbb{H}^2 \times \mathbb{H}^2\) ⋮ Uniform sublevel Radon-like inequalities ⋮ On the Wolff circular maximal function ⋮ Quasi-extremals for convolution with surface measure on the sphere ⋮ Averages in vector spaces over finite fields ⋮ Geometric incidence theorems via Fourier analysis ⋮ From harmonic analysis to arithmetic combinatorics

Cites Work

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• Averages in the plane over convex curves and maximal operators
• Two endpoint bounds for generalized Radon transforms in the plane
• Generalizations of Riesz potentials and \(L^ p\) estimates for certain k- plane transforms
• Sharp local well-posedness results for the nonlinear wave equation
• Combinatorial complexity bounds for arrangements of curves and spheres
• Hilbert integrals, singular integrals, and Radon transforms. I
• Propagation of singularities and maximal functions in the plane
• Wave front sets, local smoothing and Bourgain's circular maximal theorem
• On some variants of the Kakeya problem
• Local smoothing type estimates on \(L^p\) for large \(p\)
• A general rearrangement inequality for multiple integrals
• A geometric proof of the circular maximal theorem
• Packing Circles in the Plane
• Multilinear proofs for two theorems on circular averages
• A Kakeya-type problem for circles
• Convolution with measures on hypersurfaces
• A generalization of Bourgain’s circular maximal theorem

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