Geodesic
Weighted endpoint estimates for commutators of fractional integrals
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 153-160 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Given $\alpha $, $0\alpha $, and $b\in {\mathrm BMO}$, we give sufficient conditions on weights for the commutator of the fractional integral operator, $[b,I_\alpha ]$, to satisfy weighted endpoint inequalities on $\mathbb{R}^n$ and on bounded domains. These results extend our earlier work [3], where we considered unweighted inequalities on $\mathbb{R}^n$.
Given $\alpha $, $0\alpha $, and $b\in {\mathrm BMO}$, we give sufficient conditions on weights for the commutator of the fractional integral operator, $[b,I_\alpha ]$, to satisfy weighted endpoint inequalities on $\mathbb{R}^n$ and on bounded domains. These results extend our earlier work [3], where we considered unweighted inequalities on $\mathbb{R}^n$.
Classification : 26A33, 42B20, 42B25
Keywords: fractional integrals; commutators; BMO; weights; Orlicz spaces; maximal functions 
@article{CMJ_2007_57_1_a12,
     author = {Cruz-Uribe, D., SFO and Fiorenza, A.},
     title = {Weighted endpoint estimates for commutators of fractional integrals},
     journal = {Czechoslovak Mathematical Journal},
     pages = {153--160},
     year = {2007},
     volume = {57},
     number = {1},
     mrnumber = {2309956},
     zbl = {1174.42013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a12/}
}
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Cruz-Uribe, D., SFO; Fiorenza, A. Weighted endpoint estimates for commutators of fractional integrals. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 153-160. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a12/