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Rough oscillatory singular integrals on ℝⁿ

Hussain Mohammad Al-QassemLeslie ChengYibiao Pan — 2014

Studia Mathematica

We establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. The kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log deg(P), which is optimal and was first obtained by Papadimitrakis and Parissis (2010) for kernels without any radial roughness. Among key ingredients of our methods are an L¹ → L² estimate and extrapolation.

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