Calculus for Fourier Integral Operators in generalized SG classes

TL;DR

This paper develops a calculus for generalized SG Fourier integral operators without requiring phase homogeneity, and proves their boundedness on L^2 spaces for regular phases and bounded amplitudes.

Contribution

It extends the calculus of SG Fourier integral operators to broader classes without phase homogeneity and establishes their L^2 boundedness.

Findings

Extended calculus for SG Fourier integral operators.

Proved L^2 boundedness for operators with regular phases.

Applicable to broader classes of symbols and phases.

Abstract

We construct a calculus for generalized $\mathbf{SG}$ Fourier integral operators, extending known results to a broader class of symbols of $\mathbf{SG}$ type. In particular, we do not require that the phase functions are homogeneous. We also prove the $L^2(\mathbf{R}^{d})$-boundedness of the generalized $\mathbf{SG}$ Fourier integral operators having regular phase functions and amplitudes uniformly bounded on $\mathbf{R}^{2d}$.