L^p-estimates for singular integral operators along codimension one subspaces

2025/02/18 by Flórez-Amatriain, Mikel
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.13079

Abstract

In this paper we study maximal directional singular integral operators in ℝⁿ given by a Hörmander--Mihlin multiplier on an (n-1)-dimensional subspace and acting trivially in the perpendicular direction. The subspace is allowed to depend measurably on the first n-1 variables of ℝⁿ . Assuming the subspace to be non degenerate in the sense that it is away from a cone around e_n and the function f to be frequency supported in a cone away from ℝ^n-1 , we prove L^p -bounds for these operators for p > 3/2 . If we assume, additionally, that \widehatf is supported in a single frequency band, we are able to extend the boundedness range to p >1 . The non-degeneracy assumption cannot in general be removed, even in the band-limited case.

Related

• Off-diagonal and pointwise estimates for compact Calderon-Zygmund operators
• Uniform estimates on multi-linear operators with modulation symmetry
• Logarithmic L^p bounds for maximal directional singular integrals in the\n plane
• L^p bounds for singular integrals and maximal singular integrals with\n rough kernels
• Multilinear singular integrals on non-commutative L^p spaces