Geodesic
The continuity of multilinear singular integral operators with variable Calder\'on--Zygmund kernel on Hardy and Herz Spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 156-166.

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We prove the continuity of some multilinear operators generated by singular integral operators with variable Calderón–Zygmund kernel and Lipschitz functions on some Hardy and Herz-type spaces. 
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Liu Lanzhe. The continuity of multilinear singular integral operators with variable Calder\'on--Zygmund kernel on Hardy and Herz Spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 156-166. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a10/

[1] A. P. Calderón and A. Zygmund, “On singular integrals with variable kernels”, Appl. Anal., 7 (1978), 221–238 | DOI | MR | Zbl

[2] W. G. Chen, “Besov estimates for a class of multilinear singular integrals”, Acta Math. Sinica, 16 (2000), 613–626 | DOI | MR | Zbl

[3] F. Chiarenza, M. Frasca and P. Longo, “Interior $W^{2,p}$-estimates for nondivergence elliptic equations with discontinuous coefficients”, Ricerche Mat., 40 (1991), 149–168 | MR | Zbl

[4] J. Cohen, “A sharp estimate for a multilinear singular integral on $R^n$”, Indiana Univ. Math. J., 30 (1981), 693–702 | DOI | MR | Zbl

[5] J. Cohen and J. Gosselin, “On multilinear singular integral operators on $R^n$”, Studia Math., 72 (1982), 199–223 | MR

[6] J. Cohen and J. Gosselin, “A BMO estimate for multilinear singular integral operators”, Illinois J. Math., 30 (1986), 445–465 | MR

[7] R. Coifman and Y. Meyer, Wavelets, Calderón–Zygmund and multilinear operators, Cambridge Studies in Advanced Math., 48, Cambridge University Press, Cambridge, 1997 | MR | Zbl

[8] R. Coifman, R. Rochberg and G. Weiss, “Factorization theorems for Hardy spaces in several variables”, Ann. of Math., 103 (1976), 611–635 | DOI | MR | Zbl

[9] Y. Ding and S. Z. Lu, “Weighted boundedness for a class rough multilinear operators”, Acta Math. Sinica, 17 (2001), 517–526 | DOI | MR | Zbl

[10] G. Di Fazio and M. A. Ragusa, “Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients”, J. Func. Anal., 112 (1993), 241–256 | DOI | MR | Zbl

[11] J. Garcia-Cuerva and M. L. Herrero, “A theory of Hardy spaces associated to the Herz spaces”, Proc. London Math. Soc., 69 (1994), 605–628 | DOI | MR | Zbl

[12] J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Math., 16, Amsterdam, 1985 | MR

[13] S. Janson, “Mean oscillation and commutators of singular integral operators”, Ark. Math., 16 (1978), 263–270 | DOI | MR | Zbl

[14] S. Z. Lu, H. X. Wu and P. Zhang, “Multilinear singular integrals with rough kernel”, Acta Math. Sinica, 19 (2003), 51–62 | DOI | MR | Zbl

[15] S. Z. Lu, Q. Wu and D. C. Yang, “Boundedness of commutators on Hardy type spaces”, Sci. in China (ser. A), 45 (2002), 984–997 | DOI | MR | Zbl

[16] S. Z. Lu and D. C. Yang, “The decomposition of the weighted Herz spaces and its applications”, Sci. in China (ser. A), 38 (1995), 147–158 | MR

[17] S. Z. Lu and D. C. Yang, “The weighted Herz type Hardy spaces and its applications”, Sci. in China (ser. A), 38 (1995), 662–673 | MR | Zbl

[18] S. Z. Lu, D. C. Yang and Z. S. Zhou, “Oscillatory singular integral operators with Calderón–Zygmund kernels”, Southeast Asian Bull. of Math., 23 (1999), 457–470 | MR | Zbl

[19] M. Paluszynski, “Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss”, Indiana Univ. Math. J., 44 (1995), 1–17 | DOI | MR | Zbl

[20] E. M. Stein, Harmonic Analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton NJ, 1993 | MR | Zbl