The best constant for the centered Hardy–Littlewood maximal inequality

Antonios D. Melas

Type: Article

Publication Date: 2003-03-01

Citations: 108

DOI: https://doi.org/10.4007/annals.2003.157.647

Abstract

We find the exact value of the best possible constant C for the weak-type (1, 1) inequality for the one-dimensional centered Hardy-Littlewood maximal operator.We prove that C is the largest root of the quadratic equation 12C 2 -22C + 5 = 0 thus obtaining C = 1.5675208 . . . .This is the first time the best constant for one of the fundamental inequalities satisfied by a centered maximal operator is precisely evaluated.

Locations

arXiv (Cornell University) - View - PDF
Annals of Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+	The best constant for centered Hardy-Littlewood maximal inequality	2003	Antonios D. Melas
+	The best constant for the centered maximal operator on radial functions	2009	J. M. Aldaz J. Pérez Lázaro
+	The best constant for the centered maximal operator on radial decreasing functions	2009	J. M. Aldaz J. Pérez Lázaro
+ PDF Chat	The best constant for the centered maximal operator on radial decreasing functions	2011	J. M. Aldaz J. Pérez Lázaro
+ PDF Chat	On the centered Hardy-Littlewood maximal operator	2002	Antonios D. Melas
+ PDF Chat	Lower Bounds and Fixed Points for the Centered Hardy–Littlewood Maximal Operator	2019	Samuel Zbarsky
+ PDF Chat	A remark on the centered n-dimensional Hardy-Littlewood maximal function	2000	J. M. Aldaz
+	Chapter 1: The Hardy-Littlewood maximal operator	2018
+	Lower bounds and fixed points for the centered Hardy--Littlewood maximal operator	2019	Samuel Zbarsky
+	Lower bounds and fixed points for the centered Hardy--Littlewood maximal operator	2019	Samuel Zbarsky
+	The sharp constant for truncated Hardy-Littlewood maximal inequality	2021	Jia Wu Shao Liu Mingquan Wei Dunyan Yan
+ PDF Chat	Centered Hardy–Littlewood maximal operator on the real line: Lower bounds	2019	Paata Ivanisvili Samuel Zbarsky
+	Lower bounds for the centered Hardy-Littlewood maximal operator on the real line	2020	J. Pérez Lázaro
+	Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level	2021	Cristian González-Riquelme
+	The one-sided dyadic Hardy—Littlewood maximal operator	2014	María Lorente F. J. Martín-Reyes
+	The hardy-littlewood maximal operator	1983	Jean-Lin Journé
+	The Hardy-Littlewood maximal operator	1975	Miguel de Guzmán
+ PDF Chat	A note on Hardy-Littlewood maximal operators	2016	Mingquan Wei Xudong Nie Di Wu Dunyan Yan
+	Weights for the one-side Hardy-Littlewood maximal functions	1991	Francisco Reyes
+	Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level	2023	Cristian González-Riquelme

Works That Cite This (107)

Action	Title	Year	Authors
+	Centered Hardy–Littlewood maximal functions on H-type groups revisited	2024	Cheng Bi Hong-Quan Li Ye Zhang
+ PDF Chat	Limiting weak-type behavior for the Riesz transform and maximal operator when λ → ∞	2007	Prabhu Janakiraman
+ PDF Chat	The Norm of the Fourier Transform on Compact or Discrete Abelian Groups	2020	Mokshay Madiman Peng Xu
+	On a Generalization of the Hermite–Hadamard Inequality and Applications in Convex Geometry	2020	Bernardo González Merino
+	Limiting weak-type behaviors for Riesz transforms and maximal operators in Bessel setting	2019	Xianming Hou Huoxiong Wu
+ PDF Chat	The best constant for the centered maximal operator on radial decreasing functions	2011	J. M. Aldaz J. Pérez Lázaro
+	Random Martingales and localization of maximal inequalities	2009	Assaf Naor Terence Tao
+	Sharp bounds for m-linear Hardy and Hilbert Operators	2012	Zunwei Fu Loukas Grafakos Shan Zhen Lu Fayou Zhao
+	Best constants for the Hardy–Littlewood maximal operator on finite graphs	2015	Javier Soria Pedro Tradacete
+	Harmonic-Hardy Spaces hp(ℍ)	2015	Ali Taheri

Works Cited by This (13)

Action	Title	Year	Authors
+	Real Variable Methods in Fourier Analysis	1981	Miguel de Guzmán
+	Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals	2002	Elias M. Stein Timothy S Murphy
+ PDF Chat	On the centered Hardy-Littlewood maximal operator	2002	Antonios D. Melas
+	A note on the one-dimensional maximal function	1989	Antonio Bernal
+	A New Proof of the Hardy-Littlewood Maximal Theorem	1984	Hasse Carlsson
+ PDF Chat	On a covering problem related to the centered Hardy-Littlewood maximal inequality	2003	Antonios D. Melas
+	Best Constants for Uncentred Maximal Functions	1997	Loukas Grafakos Stephen Montgomery-Smith
+	Weak type (1, 1) inequalities of maximal convolution operators	1992	M. Trinidad Menárguez Fernando Soria
+	Research Problems in Complex Analysis	1989	David A. Brannan W. K. Hayman
+	Remarks on the Hardy–Littlewood maximal function	1998	J. M. Aldaz