On families between the Hardy–Littlewood and spherical maximal functions

Dosidis, Georgios; Grafakos, Loukas

doi:10.4310/arkiv.2021.v59.n2.a4

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Proof Of Theorem 111

Introduction1

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2022

2024

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Cited by 4 publications

(2 citation statements)

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“…An important obstacle we address is the pointwise definition of the maximal operator (see (1.3)) for general functions. This definition can be given via an abstract extension (see [11]), but this is not as useful for our purposes. We provide below a concrete approach that preserves the pointwise bounds provided by the supremum.…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

On pointwise a.e. convergence of multilinear operators

Grafakos¹,

He²,

Honzík³

et al. 2023

Can. J. Math.-J. Can. Math.

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In this work, we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) the doubly truncated homogeneous singular integral operators associated with $L^q$ functions on the sphere and (b) lacunary multiplier operators of limited smoothness. The a.e. convergence is deduced from the $L^2\times \cdots \times L^2\to L^{2/m}$ boundedness of the associated maximal multilinear operators.

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Section: Proof Of Theorem 11mentioning

confidence: 99%