The variation of the maximal function of a radial function

Hannes Luiro

Type: Article

Publication Date: 2018-01-01

Citations: 56

DOI: https://doi.org/10.4310/arkiv.2018.v56.n1.a9

Abstract

It is shown for the non-centered Hardy–Littlewood maximal operator $M$ that ${\lVert DMf \rVert}_1 \: \leq C_n \: {\lVert Df \rVert}_1$ for all radial functions in $W^{1,1} (\mathbb{R}^n)$.

Locations

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

Similar Works

Action	Title	Year	Authors
+	The variation of the maximal function of a radial function	2017	Hannes Luiro
+	The variation of the maximal function of a radial function	2017	Hannes Luiro
+	The Variation of the Fractional Maximal Function of a Radial Function	2017	Hannes Luiro José Madrid
+	The Variation of the Fractional Maximal Function of a Radial Function	2017	Hannes Luiro José Madrid
+ PDF Chat	The Variation of the Fractional Maximal Function of a Radial Function	2017	Hannes Luiro José Madrid
+	On the variation of the Hardy-Littlewood maximal function	2015	Ondřej Kurka
+ PDF Chat	Continuity of the gradient of the fractional maximal operator on $W^{1,1} (\mathbb{R}^d)$	2023	David Beltran Cristian González-Riquelme José Madrid Julian Weigt
+	Continuity of the gradient of the fractional maximal operator on $W^{1,1}(\mathbb{R}^d)$	2021	David Beltran Cristian González-Riquelme José Madrid Julian Weigt
+ PDF Chat	Continuity of the maximal operator in Sobolev spaces	2006	Hannes Luiro
+	Regularity of the centered fractional maximal function on radial functions	2019	David Beltrán José Madrid
+	Regularity of the centered fractional maximal function on radial functions	2019	David Beltran José Madrid
+ PDF Chat	Weak-type Estimates in Morrey Spaces for Maximal Commutator and Commutator of Maximal Function	2018	Müjdat Ağcayazı Амиран Гогатишвили Rza Mustafayev
+	The hardy-littlewood maximal function of a sobolev function	1997	Juha Kinnunen
+	Regularity of the centered fractional maximal function on radial functions	2020	David Beltran José Madrid
+ PDF Chat	Gradient bounds for radial maximal functions	2021	Emanuel Carneiro Cristian González-Riquelme
+ PDF Chat	A Note on Boundedness of the Hardy–Littlewood Maximal Operator on Morrey Spaces	2015	Амиран Гогатишвили Rza Mustafayev
+	Spherical maximal operators on radial functions	1996	Andreas Seeger Stephen Wainger James Wright
+	Spherical maximal operators on radial functions	1996	Andreas Seeger Stephen Wainger James Wright
+ PDF Chat	An Estimate for the Kakeya Maximal Operator on Functions of Square Radial Type	1999	Hitoshi Tanaka
+	The Hardy–Littlewood maximal function	2014	Omar El-Fallah Karim Kellay Javad Mashreghi Thomas Ransford

Works That Cite This (56)

Action	Title	Year	Authors
+	On the variation of the Hardy–Littlewood maximal functions on finite graphs	2020	Feng Liu Qingying Xue
+	Weak differentiability for fractional maximal functions of general L functions on domains	2020	João P. G. Ramos Olli Saari Julian Weigt
+ PDF Chat	Variation of the uncentered maximal characteristic function	2021	Julian Weigt
+	Variation of the uncentered maximal characteristic Function	2020	Julian Weigt
+ PDF Chat	Endpoint Sobolev bounds for fractional Hardy–Littlewood maximal operators	2022	Julian Weigt
+ PDF Chat	Variation of the Dyadic Maximal Function	2022	Julian Weigt
+	The one-dimensional centred maximal function diminishes the variation of indicator functions	2021	Constantin Bilz Julian Weigt
+	The Variation of the Uncentered Maximal Operator with respect to Cubes	2021	Julian Weigt
+ PDF Chat	Gradient bounds for radial maximal functions	2021	Emanuel Carneiro Cristian González-Riquelme
+	The Variation of the Fractional Maximal Function of a Radial Function	2017	Hannes Luiro José Madrid

Works Cited by This (6)

Action	Title	Year	Authors
+	Nonlinear Potential Theory of Degenerate Elliptic Equations	2018	Juha Heinonen Tero Kilpeläinen Олли Мартио
+ PDF Chat	A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function	2002	Hitoshi Tanaka
+ PDF Chat	Continuity of the maximal operator in Sobolev spaces	2006	Hannes Luiro
+	The hardy-littlewood maximal function of a sobolev function	1997	Juha Kinnunen
+	ON BOUNDEDNESS OF MAXIMAL FUNCTIONS IN SOBOLEV SPACES	2004	Piotr Hajłasz Jani Onninen
+	On the variation of the Hardy-Littlewood maximal function	2015	Ondřej Kurka