English

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 Lp(V2)L^p(V_2) 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.

Keywords

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

R2 v1 2026-07-01T10:39:51.062Z