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arXiv · 2602.15528

A lower bound for a variation norm operator associated with circular means

David Beltran·Anthony Carbery·Luz Roncal·Andreas Seeger
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Abstract

We prove that a local $L^p(V_2)$ 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.

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David Beltran, Anthony Carbery, Luz Roncal, Andreas Seeger. 2026-02-17. A lower bound for a variation norm operator associated with circular means. https://arxiv.org/abs/2602.15528

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