L¹ Boundedness of a class of rough Fourier integral operators

Abstract

In this note, we consider a class of Fourier integral operators with rough amplitudes and rough phases. When the index of symbols in some range, we prove that they are bounded on L^1 and construct an example to show that this result is sharp in some cases. This result is a generalization of the corresponding theorems of Kenig-Staubach and Dos Santos Ferreira-Staubach.

Keywords

Fourier integral operators / amplitude / phase

References

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Higher Education Press 2023