In this paper we introduce atomic Hardy spaces on the product domain $S^{n-1}×S^{m-1}$ and prove that rough singular integral operators with Hardy space function kernels are $L^p$ bounded on $ℝ^{n} × ℝ^{m}$. This is an extension of some well known results.
Department of Mathematics, Nanchang Vocational and Technical Teachers' College, Nanchang, Jiangxi, 330013 P.R. China
Bibliografia
[1] J. Duoandikoetxea, Multiple singular integrals and maximal functions along hypersurfaces, Ann. Inst. Fourier (Grenoble) 36 (4) (1986), 185-206.
[2] J. Duoandikoetxea and J. L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), 541-561.
[3] R. Fefferman, Singular integrals on product domains, Bull. Amer. Math. Soc. 4 (1981), 195-201.
[4] Y. S. Jiang and S. Z. Lu, A class of singular integral operators with rough kernel on product domains, Hokkaido Math. J. 24 (1995), 1-7.
[5] D. K. Watson, The Hardy space kernel condition for rough integrals, preprint.
Typ dokumentu
Bibliografia
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