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.

Key words： Fourier integral operators; amplitude; phase

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11871436) and the National Key Research and Development Program of China (No. 2022YFA1005700)

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