On differentiation of integrals

DOI10.1073/pnas.74.6.2211zbMath0374.28002OpenAlexW1970386123WikidataQ35062989 ScholiaQ35062989MaRDI QIDQ4152783

Antonio Córdoba, Robert A. Fefferman

Publication date: 1977

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.74.6.2211

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Abstract differentiation theory, differentiation of set functions (28A15)

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(Un)boundedness of directional maximal operators through a notion of “Perron capacity” and an application ⋮ On unboundedness of maximal operators for directional Hilbert transforms ⋮ A remark on a maximal function over a Cantor set of directions ⋮ \(L^2\) bounds for a maximal directional Hilbert transform ⋮ Sharp \(L^{2}\) bound of maximal Hilbert transforms over arbitrary sets of directions ⋮ Maximal functions along convex curves with lacunary directions ⋮ Differentiating Orlicz spaces with rectangles having fixed shapes in a set of directions ⋮ Covering lemmas revisited ⋮ Weighted and unweighted Solyanik estimates for the multilinear strong maximal function ⋮ Some recent developments in Fourier analysis and 𝐻^{𝑝}-theory on product domains ⋮ Application of Perron trees to geometric maximal operators ⋮ Differentiating Orlicz spaces with rare bases of rectangles ⋮ Kakeya-type sets for geometric maximal operators ⋮ Weighted estimates for conic Fourier multipliers ⋮ 𝐁𝐌𝐎 on shapes and sharp constants ⋮ On a conjecture of E. M. Stein on the Hilbert transform on vector fields ⋮ Differentiation of integrals in higher dimensions ⋮ The development of square functions in the work of A. Zygmund ⋮ $L^p$ estimates for maximal averages along one-variable vector fields in ${\mathbf R} ^2$ ⋮ Kakeya sets and directional maximal operators in the plane ⋮ Problems in harmonic analysis related to curvature ⋮ Directional maximal operators with smooth densities ⋮ Maximal Operators Associated to Sets of Directions of Hausdorff and Minkowski Dimension Zero ⋮ Maximal subspace averages ⋮ Maximal directional operators along algebraic varieties

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