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- W4225529199 abstract "Given a family G of rectangles, to which one associates a tree [G], one defines a natural number $lambda$ [G] called its analytic split and satisfying, for all 1 < p < $infty$ log($lambda$ [G]) p MG p p where MG is the Hardy-Littlewood type maximal operator associated to the family G. As an application, we completely characterize the boundeness of planar rarefied directional maximal operators on L p for 1 < p < $infty$. Precisely, if $Omega$ is an arbitrary set of angles in [0, $pi$ 4), we prove that any rarefied basis B of the directional basis R $Omega$ yields an operator MB that has the same L p-behavior than the directional maximal operator M $Omega$ for 1 < p < $infty$." @default.
- W4225529199 created "2022-05-05" @default.
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- W4225529199 date "2022-04-01" @default.
- W4225529199 modified "2023-09-30" @default.
- W4225529199 title "Kakeya-type sets for Geometric Maximal Operators" @default.
- W4225529199 doi "https://doi.org/10.48550/arxiv.2204.00253" @default.
- W4225529199 hasPublicationYear "2022" @default.
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