Medians, continuity, and vanishing oscillation

Jonathan Poelhuis, Alberto Torchinsky

Type: Article

Publication Date: 2012-01-01

Citations: 24

DOI: https://doi.org/10.4064/sm213-3-3

Abstract

We consider properties of medians as they pertain to the continuity and vanishing oscillation of a function. Our approach is based on the observation that medians are related to local sharp maximal functions restricted to a cube of $\mathbb R^n$.

Locations

Studia Mathematica - View - PDF

Similar Works

Action	Title	Year	Authors
+	Medians, Continuity, and Oscillation	2012	Jonathan Poelhuis Alberto Torchinsky
+	Medians, Continuity, and Oscillation	2012	Jonathan Poelhuis Alberto Torchinsky
+ PDF Chat	Median-Type John–Nirenberg Space in Metric Measure Spaces	2022	Kim Myyryläinen
+	Mean Oscillation Over Cubes and Holder Continuity	1964	Norman G. Meyers
+ PDF Chat	Mean oscillation over cubes and Hölder continuity	1964	Norman G. Meyers
+ PDF Chat	On properties of functions with conditions on their mean oscillation over cubes	1982	Tord Sjödin
+	Geometric medians	1992	Joseph Gil William Steiger Avi Wigderson
+	The median and its extensions	2011	Gleb Beliakov Humberto Bustince Javier Fernández
+	Median-type John-Nirenberg space in metric measure spaces	2021	Kim Myyryläinen
+	Local sharp maximal functions	1985	Björn Jawerth Alberto Torchinsky
+	Median values, 1-harmonic functions, and functions of least gradient	2012	Matthew Rudd Heather A. Van Dyke
+	Limits and Continuity of Functions	2004
+	Limits and Continuity of Functions	2005
+	Limits and Continuity of Functions	2016	Tunc Geveci
+	Limits and Continuity of Functions	2017	Steven G. Krantz
+	Limits and Continuity of Functions	2022	Bertrand Russell
+	Limits and Continuity of Functions	2022	Steven G. Krantz
+ PDF Chat	A decomposition of functions with vanishing mean oscillation	2001	Michael Brian Korey
+	Limits, Continuity, and Elementary Functions	2017	Paul Loya
+	Mean modulus of oscillation and piecewise monotone approximation	1982	Evgenii Alexandrovich Sevast'yanov

Works That Cite This (24)

Action	Title	Year	Authors
+ PDF Chat	John–Nirenberg inequalities for parabolic BMO	2022	Juha Kinnunen Kim Myyryläinen Dachun Yang
+	Fractional Medians and Their Maximal Functions	2024	Yohei Tsutsui
+ PDF Chat	Lebesgue Points of Besov and Triebel–Lizorkin Spaces with Generalized Smoothness	2021	Ziwei Li Dachun Yang Wen Yuan
+ PDF Chat	Capacity in Besov and Triebel–Lizorkin spaces with generalized smoothness	2024	Nijjwal Karak Debarati Mondal
+ PDF Chat	Generalized Lebesgue points for Sobolev functions	2017	Nijjwal Karak
+ PDF Chat	Triebel-Lizorkin capacity and hausdorff measure in metric spaces	2020	Nijjwal Karak
+ PDF Chat	Approximation by Hölder Functions in Besov and Triebel–Lizorkin Spaces	2016	Toni Heikkinen Heli Tuominen
+	Triebel–Lizorkin capacity and Hausdorff measure in metric spaces with chain condition	2024	Debarati Mondal Nijjwal Karak
+	Generalized Lebesgue Points for Hajłasz Functions	2018	Toni Heikkinen
+ PDF Chat	The Besov capacity in metric spaces	2016	Juho Nuutinen

Works Cited by This (11)

Action	Title	Year	Authors
+	Functions of Vanishing Mean Oscillation	1987	Xianliang Shi Alberto Torchinsky
+ PDF Chat	Functions of vanishing mean oscillation	1975	Donald Sarason
+ PDF Chat	Bounded mean oscillation with Orlicz norms and duality of Hardy spaces	1976	Jan-Olov Strömberg
+	A pointwise estimate for the local sharp maximal function with applications to singular integrals	2010	Andrei K. Lerner
+ PDF Chat	A Simple Proof of the A2 Conjecture	2012	Andrei K. Lerner
+	Quasi-Isometric Mappings	1985	Floyd I. John
+	Some function spaces defined using the mean oscillation over cubes	1965	Sven Spanne
+	Local sharp maximal functions	1985	Björn Jawerth Alberto Torchinsky
+ PDF Chat	Functions of Vanishing Mean Oscillation	1975	Donald Sarason
+	Local Sharp Maximal Functions	2014	Björn Jawerth Alberto Torchinsky