The Hardy space H^1_{FIO}(R^n) for Fourier integral operators equals its Littlewood-Paley g-function, maximal-function, and G*_alpha versions for alpha > 2, with equivalent norms.
Characterizations of Hardy spaces for Fourier integral operators
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abstract
We prove several characterizations of the Hardy spaces for Fourier integral operators $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$, for $1<p<\infty$. First we characterize $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ in terms of $L^{p}(\mathbb{R}^{n})$-norms of parabolic frequency localizations. As a corollary, any characterization of $L^{p}(\mathbb{R}^{n})$ yields a corresponding version for $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$. In particular, we obtain a maximal function characterization and a characterization in terms of vertical square functions.
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math.AP 1years
2019 1verdicts
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Characterizations of the Hardy space $\mathcal{H}_{FIO}^{1}(\mathbb{R}^{n})$ for Fourier integral operators
The Hardy space H^1_{FIO}(R^n) for Fourier integral operators equals its Littlewood-Paley g-function, maximal-function, and G*_alpha versions for alpha > 2, with equivalent norms.