Directional operators and radial functions on the plane

DOI10.1007/BF02559710zbMath0852.47014MaRDI QIDQ1915861

Javier Duoandikoetxea, Ana M. Vargas

Publication date: 1 July 1996

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

Minkowski dimensionHardy-Littlewood maximal functionmaximal Hilbert transform

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Linear operators on function spaces (general) (47B38)

Related Items (5)

Kakeya-type sets over Cantor sets of directions in \(\mathbb {R}^{d+1}\) ⋮ Logarithmic \(L^p\) bounds for maximal directional singular integrals in the plane ⋮ Problems on pointwise convergence of solutions to the Schrödinger equation ⋮ Kakeya sets and directional maximal operators in the plane ⋮ Maximal operators associated to Fourier multipliers with an arbitrary set of parameters

Cites Work

• The behaviour on radial functions of maximal operators along arbitrary directions and the Kakeya maximal operator
• Littlewood-Paley decompositions and Fourier multipliers with singularities on certain sets
• The multiplier problem for the polygon
• Maximal functions associated to rectangles with uniformly distributed directions
• Differentiation in lacunary directions
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