Medians, Continuity, and Oscillation
Jonathan Poelhuis, Alberto Torchinsky
TL;DR
This paper explores how medians relate to the continuity and oscillation of functions, using their connection to local sharp maximal functions within cubes in al^n.
Contribution
It introduces a novel approach linking medians to local sharp maximal functions to analyze function continuity and oscillation.
Findings
Medians are related to local sharp maximal functions.
Properties of medians influence function continuity.
Analysis of oscillation using median-based methods.
Abstract
In this paper 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 .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Advanced Harmonic Analysis Research