Strongly singular integrals on stratified groups

2018/10/17 by Paolo Ciatti, James Wright, Ciatti, Paolo +1
Mathematics · #35P99 (secondary) #42B15 #42B20 #43A22 (primary) #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1810.07540

openalex publication_date 2018/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of spectral multipliers on stratified Lie groups which generalise the class of Hörmander multipliers and include multipliers with an oscillatory factor. Oscillating multipliers have been examined extensively in the euclidean setting where sharp, endpoint L^p estimates are well known. In the Lie group setting, corresponding L^p bounds for oscillating spectral multipliers have been established by several authors but only in the open range of exponents. In this paper we establish the endpoint L^p(G) bound when G is a stratified Lie group. More importantly we begin to address whether these estimates are sharp.

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