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A class of multi-parameter Fourier integral operators: endpoint Hardy space bounds

Published 24 Jan 2024 in math.CA and math.AP | (2401.13482v2)

Abstract: In this paper we study a class of Fourier integral operators, whose symbols lie in the multi-parameter H\"ormander class $S{\vec m}( \mathbb{R}\vn)$, where ~$\vec m=(m_1,m_2,\dots,m_d)$ is the order. We show that if in addition the phase function $\Phi(x,\xi)$ can be written as $\Phi(x,\xi)=\sum_{i=1}d\Phi_i(x_i,\xi_i)$, and each $\Phi_i(x_i,\xi_i)$ satisfies the non-degeneracy condition, then such Fourier integral operators with order ~$\vec m=(-(n_1-1)/2, -(n_2-1)/2,\dots, -(n_d-1)/2)$ are actually bounded from rectangular Hardy space $H_{rect}1(\mathbb{R}\vn)$ to $L1( \mathbb{R}n )$.

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Authors (1)

  1. Jinhua Cheng 

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