Sparse domination via the helicoidal method

2017/07/18 by Cristina Benea, Benea, Cristina, Camil Muscalu +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.1707.05484

openalex publication_date 2017/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using exclusively the localized estimates upon which the helicoidal method was built, we show how sparse estimates can also be obtained. This approach yields a sparse domination for multiple vector-valued extensions of operators as well. We illustrate these ideas for an n-linear Fourier multiplier whose symbol is singular along a k-dimensional subspace of Γ=\lbrace ξ₁+…+ξ_n+1=0 \rbrace, where k

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