Geodesic
Mean Oscillation and Boundedness of Multilinear Integral Operators with General Kernels
Archivum mathematicum, Tome 50 (2014) no. 2, pp. 77-96 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are proved. The integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are proved. The integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.
DOI : 10.5817/AM2014-2-77
Classification : 42B20, 42B25
Keywords: multilinear operator; singular integral operator; BMO space; Orlicz space; Littlewood-Paley operator; Marcinkiewicz operator; Bochner-Riesz operator 
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Lanzhe, Liu. Mean Oscillation and Boundedness of Multilinear Integral Operators with General Kernels. Archivum mathematicum, Tome 50 (2014) no. 2, pp. 77-96. doi: 10.5817/AM2014-2-77

[1] Chang, D.C., Li, J.F., Xiao, J.: Weighted scale estimates for Calderón-Zygmund type operators. Contemp. Math. 446 (2007), 61–70. | DOI | MR

[2] Chanillo, S.: A note on commutators. Indiana Univ. Math. J. 31 (1982), 7–16. | DOI | MR | Zbl

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

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

[5] Cohen, J., Gosselin, J.: A $\operatorname{BMO}$ estimate for multilinear singular integral operators. Illinois J. Math. 30 (1986), 445–465. | MR

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

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

[8] Garcia-Cuerva, J., Rubio de Francia, J.L.: Weighted norm inequalities and related topics. North-Holland Math., vol. 116, Amsterdam, 1985. | MR

[9] Janson, S.: Mean oscillation and commutators of singular integral operators. Ark. Mat. 16 (1978), 263–270. | DOI | MR | Zbl

[10] Lin, Y.: Sharp maximal function estimates for Calderón-Zygmund type operators and commutators. Acta Math. Scientia 31(A) (2011), 206–215. | MR | Zbl

[11] Liu, L.Z.: Continuity for commutators of Littlewood-Paley operator on certain Hardy spaces. J. Korean Math. Soc. 40 (2003), 41–60. | DOI | MR

[12] Liu, L.Z.: The continuity of commutators on Triebel-Lizorkin spaces. Integral Equations Operator Theory 49 (2004), 65–76. | DOI | MR | Zbl

[13] Liu, L.Z.: Endpoint estimates for multilinear integral operators. J. Korean Math. Soc. 44 (2007), 541–564. | DOI | MR | Zbl

[14] Liu, L.Z.: Sharp and weighted inequalities for multilinear integral operators. Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 101 (2007), 99–111. | MR | Zbl

[15] Liu, L.Z.: Sharp maximal function estimates and boundedness for commutators associated with general integral operator. Filomat 25 (2011), 137–151. | DOI | MR | Zbl

[16] Liu, L.Z.: Weighted boundedness for multilinear Littlewood-Paley and Marcinkiewicz operators on Morrey spaces. J. Contemp. Math. Anal. 46 (2011), 49–66. | MR | Zbl

[17] Lu, S.Z.: Four lectures on real $H^p$ spaces. World Scientific, River Edge, NI, 1995. | MR

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

[19] Pérez, C., Pradolini, G.: Sharp weighted endpoint estimates for commutators of singular integral operators. Michigan Math. J. 49 (2001), 23–37. | DOI | MR

[20] Pérez, C., Trujillo-Gonzalez, R.: Sharp weighted estimates for multilinear commutators. J. London Math. Soc. 65 (2002), 672–692. | DOI | MR | Zbl

[21] Rao, M.M., Ren, Z.D.: Theory of Orlicz spaces. Textbooks in Pure and Applied Mathematics, vol. 146, Marcel Dekker, Inc., New York, 1991. | MR | Zbl

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

[23] Torchinsky, A.: Real variable methods in harmonic analysis. Pure and Applied Math., Academic Press, New York 123 (1986). | MR | Zbl

[24] Torchinsky, A., Wang, S.: A note on the Marcinkiewicz integral. Colloq. Math. 60/61 (1990), 235–243. | MR | Zbl

[25] Wu, B.S., Liu, L.Z.: A sharp estimate for multilinear Bochner-Riesz operator. Studia Sci. Math. Hungar. 42 (1) (2005), 47–59. | MR | Zbl

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