Commutators with fractional integral operators
Studia Mathematica, Tome 233 (2016) no. 3, p. 279.

Voir la notice de l'article dans European Digital Mathematics Library

We investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for μ , λ ∈ A p , q and α/n + 1/q = 1/p, the norm | | [ b , I α ] : L p ( μ p ) → L q ( λ q ) | | is equivalent to the norm of b in the weighted BMO space BMO(ν), where ν = μ λ - 1 . This work extends some of the results on this topic existing in the literature, and continues a line of investigation which was initiated by Bloom in 1985 and was recently developed further by the first author, Lacey, and Wick.
Classification : 42B20, 42B25, 42A05, 42A50, 42A61
Mots-clés : fractional integral operator, commutator, weighted inequalities, Bloom BMO 
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Irina Holmes; Robert Rahm; Scott Spencer. Commutators with fractional integral operators. Studia Mathematica, Tome 233 (2016) no. 3, p. 279. https://geodesic-test.mathdoc.fr/item/STUMA_2016__233_3_286138/