Geodesic
Weighted endpoint estimates for commutators of multilinear fractional integral operators
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 347-359
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Let $m$ be a positive integer, $0\alpha
Let $m$ be a positive integer, $0\alpha $, $\vec {b}=(b_{1},\cdots ,b_{m})\in {\rm BMO}^m$. We give sufficient conditions on weights for the commutators of multilinear fractional integral operators $\Cal {I}^{\vec {b}}_{\alpha }$ to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl., 362, (2010), 355–373.
DOI : 10.1007/s10587-012-0034-5
Classification : 42B20, 42B25
Keywords: multilinear fractional integral operators; commutator; BMO; weight; maximal operators 
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Yan, Xuefang; Xue, Limei; Li, Wenming. Weighted endpoint estimates for commutators of multilinear fractional integral operators. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 347-359. doi: 10.1007/s10587-012-0034-5

[1] Bernardis, A., Gorosito, O., Pradolini, G.: Weighted inequalities for multilinear potential operators and its commutators. Potential Anal. 35 (2011), 253-274. | DOI | MR

[2] Chen, X., Xue, Q.: Weighted estimates for a class of multilinear fractional type operators. J. Math. Anal. Appl. 362 (2010), 355-373. | DOI | MR | Zbl

[3] Christ, M., Journé, J.-L.: Polynomial growth estimates for multilinear singular integral operators. Acta Math. 159 (1987), 51-80. | DOI | MR | Zbl

[4] Cruz-Uribe, D., Fiorenza, A.: Endpoint estimates and weighted norm inequalities for commutators of fractional integrals. Publ. Mat., Barc. 47 (2003), 103-131. | DOI | MR | Zbl

[5] Cruz-Uribe, D., Fiorenza, A.: Weighted endpoint estimates for commutators of fractional integrals. Czech. Math. J. 57 (2007), 153-160. | DOI | MR | Zbl

[6] Fefferman, C., Stein, E.: $H^{p}$ spaces of several variables. Acta Math. 129 (1972), 137-193. | DOI | MR

[7] Grafakos, L.: On multilinear fractional integrals. Stud. Math. 102 (1992), 49-56. | DOI | MR | Zbl

[8] Grafakos, L., Kalton, N.: Some remarks on multilinear maps and interpolation. Math. Ann. 319 (2001), 151-180. | DOI | MR | Zbl

[9] Grafakos, L., Torres, R. H.: Multilinear Calderón-Zygmund theory. Adv. Math. 165 (2002), 124-164. | DOI | MR | Zbl

[10] Grafakos, L., Torres, R. H.: Maximal operator and weighted norm inequalities for multilinear singular integrals. Indiana Univ. Math. J. 51 (2002), 1261-1276. | DOI | MR | Zbl

[11] Kenig, C. E., Stein, E. M.: Multilinear estimates and fractional integration. Math. Res. Lett. 6 (1999), 1-15. | DOI | MR | Zbl

[12] Lerner, A. K., Ombrosi, S., Pérez, C., Torres, R. H., Trujillo-González, R.: New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory. Adv. Math. 220 (2009), 1222-1264. | DOI | MR | Zbl

[13] Moen, K.: Weighted inequalities for multilinear fractional integral operators. Collect. Math. 60 (2009), 213-238. | DOI | MR | Zbl

[14] Pradolini, G.: Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators. J. Math. Anal. Appl. 367 (2010), 640-656. | DOI | MR | Zbl

[15] Pérez, C., Pradolini, G.: Sharp weighted endpoint estimates for commutators of singular integrals. Mich. Math. J. 49 (2001), 23-37. | DOI | MR | Zbl

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