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$(L^{\infty},{\rm BMO})$ estimates and $(H^{1},L^{1})$ estimates for Fourier integral operators with symbol in $S^{m}_{0,δ}$ (2412.00409v1)
Published 30 Nov 2024 in math.CA and math.AP
Abstract: Let $T_{a,\varphi}$ be a Fourier integral operator defined with $a\in S{m}_{0,\delta}$ with $0\leq\delta<1$ and $\varphi\in \Phi{2}$ satisfying the strong non-degenerate condition. It is showed that $T_{a,\varphi}$ is a bounded operator from $L{\infty}(\mathbb{R}n)$ to ${\rm BMO}(\mathbb{R}n)$, if $$m\leq -\frac{n}{2},$$ and from $H{1}(\mathbb{R}n)$ to $L{1}(\mathbb{R}n)$, if $$m\leq -\frac{n}{2}-\frac{n}{2}\delta.$$