Differentiation of integrals in higher dimensions

DOI10.1073/pnas.1218928110zbMath1292.42010OpenAlexW2034646170WikidataQ36729575 ScholiaQ36729575MaRDI QIDQ5170957

Javier Parcet, Keith M. Rogers

Publication date: 25 July 2014

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.1218928110

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Measures and integration on abstract linear spaces (46G12) Convergence and absolute convergence of Fourier and trigonometric series (42A20)

Related Items (4)

NONCOMMUTATIVE DE LEEUW THEOREMS ⋮ Kakeya-type sets over Cantor sets of directions in \(\mathbb {R}^{d+1}\) ⋮ Weighted estimates for conic Fourier multipliers ⋮ On logarithmic bounds of maximal sparse operators

Cites Work

• Random martingales and localization of maximal inequalities
• Kakeya sets and directional maximal operators in the plane
• Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem
• Littlewood-Paley decompositions and Fourier multipliers with singularities on certain sets
• Geometric Fourier analysis
• Maximal functions associated to rectangles with uniformly distributed directions
• On the dimension of Kakeya sets and related maximal inequalities
• A remark on maximal operators along directions in \(\mathbb R^2\)
• Maximal operators over arbitrary sets of directions
• The multiplier problem for the ball
• On the equivalence between the boundedness of certain classes of maximal and multiplier operators in Fourier analysis
• On differentiation of integrals
• The Kakeya Maximal Function and the Spherical Summation Multipliers
• Differentiation in lacunary directions
• STRONG TYPE INEQUALITIES AND AN ALMOST-ORTHOGONALITY PRINCIPLE FOR FAMILIES OF MAXIMAL OPERATORS ALONG DIRECTIONS IN ${\bb R}^2$

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