Non-Degenerate Multilinear Singular Multipliers with Fractional Rank

2025/03/18 by Zhang, Jianghao
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.14635

Abstract

We establish L^p estimates for multilinear multipliers acting on (n-1)-tuples of functions on ℝ^d. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension m. The difficulty of proving L^p bounds increases with the rank (m)/(d), and our focus is on the fractional rank case (m)/(d)<(n)/(2)≤ \lceil (m)/(d)\rceil.

Related

• Multilinear singular operators with fractional rank
• Multilinear singular integrals on non-commutative L^p spaces
• L^p-estimates for singular integral operators along codimension one subspaces
• Uniform estimates on multi-linear operators with modulation symmetry
• Singular multipliers on multiscale Zygmund sets