Strongly singular integrals along curves

2006/12/20 by Norberto Laghi, Laghi, Norberto, Neil Lyall +1
Mathematics · #42B20 #44A12 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math/0612588

openalex publication_date 2006/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we obtain L² bounds for strongly singular integrals along curves in \R^d; our results both generalise and extend to higher dimensions those obtained by Chandarana in the plane. Moreover, we show that the operators in question are bounded from Llog L to weak L¹ at the critical exponent α=0.

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