Sharp variational inequalities for average operators over finite type curves in the plane

2025/01/28 by Nie, Xudong
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.16798

Abstract

The aim of this article is to establish the L^p(ℝ²)-boundedness of the variational operator associated with averaging operators defined over finite type curves in the plane. Additionally, we present the necessary conditions for the boundedness of these operators in L^p. Furthermore, to prove one of these results, we establish a mixed-norm local smoothing estimate from L⁴ to L⁴(L²) corresponding to a family of Fourier integral operators that do not uniformly satisfy the cinematic curvature condition.

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