On families between the Hardy–Littlewood and spherical maximal functions

Georgios Dosidis, Loukas Grafakos

Type: Article

Publication Date: 2021-01-01

Citations: 3

DOI: https://doi.org/10.4310/arkiv.2021.v59.n2.a4

Abstract

We study a family of maximal operators that provides a continuous link connecting the Hardy-Littlewood maximal function to the spherical maximal function.Our theorems are proved in the multilinear setting but may contain new results even in the linear case.For this family of operators we obtain bounds between Lebesgue spaces in the optimal range of exponents.

Locations

Arkiv för matematik - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (21)

Action	Title	Year	Authors
+	Radial Fourier Multipliers and Associated Maximal Functions	1985	Anthony Carbery
+	Classical Fourier Analysis	2014	Loukas Grafakos
+	Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals	2002	Elias M. Stein Timothy S Murphy
+ PDF Chat	Lacunary spherical means	1979	Calixto P. Calderón
+	Averages in the plane over convex curves and maximal operators	1986	Jean Bourgain
+	Maximal functions: Spherical means	1976	Elias M. Stein
+ PDF Chat	Discrete Analogues in Harmonic Analysis: Spherical Averages	2002	Ákos Magyar E. M. Stein Stephen Wainger
+	A geometric proof of the circular maximal theorem	1998	Wilhelm Schlag
+	Maximal functions and Fourier transforms	1986	Josè L. Rubio de Francia
+	The multilinear Marcinkiewicz interpolation theorem revisited: The behavior of the constant	2011	Loukas Grafakos Liguang Liu Shanzhen Lu Fayou Zhao