A lower bound for a variation norm operator associated with circular means
Classical Analysis and ODEs
2026-02-18 v1
Abstract
We prove that a local variation norm estimate fails for circular means in two dimensions, and quantify this failure by proving lower bounds for functions of exponential type. This is related to lower bounds for Fourier multipliers supported on annuli, of the type considered by C\'ordoba.
Cite
@article{arxiv.2602.15528,
title = {A lower bound for a variation norm operator associated with circular means},
author = {David Beltran and Anthony Carbery and Luz Roncal and Andreas Seeger},
journal= {arXiv preprint arXiv:2602.15528},
year = {2026}
}
Comments
12 pages