Geodesic
Commutators of singular integrals on spaces of homogeneous type
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 75-93 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on $L^{p}(w)$ when $w$ belongs to the Muckenhoupt’s class $A_{p}$, $p>1$. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.
In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on $L^{p}(w)$ when $w$ belongs to the Muckenhoupt’s class $A_{p}$, $p>1$. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.
Classification : 42B25
Keywords: commutators; spaces of homogeneous type; weights 
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     author = {Pradolini, Gladis and Salinas, Oscar},
     title = {Commutators of singular integrals on spaces of homogeneous type},
     journal = {Czechoslovak Mathematical Journal},
     pages = {75--93},
     year = {2007},
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     zbl = {1174.42322},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a6/}
}
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Pradolini, Gladis; Salinas, Oscar. Commutators of singular integrals on spaces of homogeneous type. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 75-93. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a6/