Oscillatory singular integrals on Hardy spaces associated with Herz spaces

Lu, Shan Zhen; Yang, Da Chun

doi:10.1090/S0002-9939-1995-1239800-5

Oscillatory singular integrals on Hardy spaces associated with Herz spaces
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by Shan Zhen Lu and Da Chun Yang PDF

Proc. Amer. Math. Soc. 123 (1995), 1695-1701 Request permission

Abstract:

In this paper, it is proved that the oscillatory singular integral operators of nonconvolution type are bounded from Hardy spaces associated with Herz spaces to Herz spaces.

References

Yong Zhuo Chen and Ka-Sing Lau, Some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), no. 2, 255–278. MR 1001460, DOI 10.1016/0022-1236(89)90097-9
José García-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39 (1989), no. 3, 499–513. MR 1002462, DOI 10.1112/jlms/s2-39.3.499
C. S. Herz, Lipschitz spaces and Bernstein’s theorem on absolutely convergent Fourier transforms, J. Math. Mech. 18 (1968/69), 283–323. MR 0438109, DOI 10.1512/iumj.1969.18.18024
Shan Zhen Lu and Da Chun Yang, The Littlewood-Paley function and $\phi$-transform characterizations of a new Hardy space $HK_2$ associated with the Herz space, Studia Math. 101 (1992), no. 3, 285–298. MR 1153785, DOI 10.4064/sm-101-3-285-298
Yibiao Pan, Hardy spaces and oscillatory singular integrals, Rev. Mat. Iberoamericana 7 (1991), no. 1, 55–64. MR 1109480, DOI 10.4171/RMI/105
D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms. I, Acta Math. 157 (1986), no. 1-2, 99–157. MR 857680, DOI 10.1007/BF02392592
Fulvio Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. I. Oscillatory integrals, J. Funct. Anal. 73 (1987), no. 1, 179–194. MR 890662, DOI 10.1016/0022-1236(87)90064-4
Da Chun Yang, Real-variable characterizations of the Hardy spaces $HK_p(\mathbf R^n)$, Adv. in Math. (China) 24 (1995), no. 1, 63–73 (Chinese, with English and Chinese summaries). MR 1334605