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.
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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.