JournalsrmiVol. 37, No. 5pp. 1717–1745

Characterizations of Hardy spaces for Fourier integral operators

  • Jan Rozendaal

    The Australian National University, Canberra, Australia
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Abstract

We prove several characterizations of the Hardy spaces for Fourier integral operators HFIOp(Rn)\mathcal{H}^{p}_{\mathrm{FIO}}(\mathbb{R}^n), for 1<p<1 < p < \infty. First we characterize HFIOp(Rn)\mathcal{H}^{p}_{\mathrm{FIO}}(\mathbb{R}^n) in terms of Lp(Rn)L^{p}(\mathbb{R}^n)-norms of parabolic frequency localizations. As a corollary, any characterization of Lp(Rn)L^{p}(\mathbb{R}^n) yields a corresponding version for HFIOp(Rn)\mathcal{H}^{p}_{\mathrm{FIO}}(\mathbb{R}^n). In particular, we obtain a maximal function characterization and a characterization in terms of vertical square functions.

Cite this article

Jan Rozendaal, Characterizations of Hardy spaces for Fourier integral operators. Rev. Mat. Iberoam. 37 (2021), no. 5, pp. 1717–1745

DOI 10.4171/RMI/1246