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Article

Keywords:
Fourier integral operator; Hardy spaces; Herz spaces
Summary:
In this paper, it is proved that the Fourier integral operators of order $m$, with $-n < m \leq -(n-1)/2$, are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.
References:
[1] Hörmander, L.: Fourier integral operators I. Acta Math. 127 (1971), 79-183. DOI 10.1007/BF02392052 | MR 0388463
[2] Lu, S., Yang, D.: The Littlewood-Paley function and $\phi$-transform characterizations of a new Hardy space $HK_2$ associated with the Herz space. Stud. Math. 101 (1992), 285-298. DOI 10.4064/sm-101-3-285-298 | MR 1153785
[3] Lu, S., Yang, D.: The decomposition of the weighted Herz spaces on $R_n$ and its applications. Sci. China Ser. A 38 (1995), 147-158. MR 1338138
[4] Lu, S., Yang, D.: The weighted Herz-type Hardy space and its applications. Sci. China Ser. A 38 (1995), 661-673. MR 1351232 | Zbl 0832.42013
[5] Marco, M. P., Silvia, S.: Boundedness of Fourier integral operators on Hardy spaces. Proc. Edinb. Math. Soc. 51 (2008), 443-463. DOI 10.1017/S001309150500012X | MR 2465918
[6] Seeger, A., Sogge, C., Stein, E.: Regularity properties of Fourier integral operators. Ann. Math. 134 (1991), 231-251. DOI 10.2307/2944346 | MR 1127475 | Zbl 0754.58037
[7] Stein, E.: Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press (1993). MR 1232192 | Zbl 0821.42001
[8] Yang, D.: The real-variable characterizations of Hardy spaces $HK_p(R^n)$. Adv. Math. 24 (1995), 63-73. MR 1334605
[9] Zhou, Y.: Boundedness of sublinear operators in Herz-type Hardy spaces. Taiwannse J. Math. 13 (2009), 983-996. DOI 10.11650/twjm/1500405453 | MR 2526352 | Zbl 1180.42009
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