Commutators with fractional integral operators

Irina Holmes; Robert Rahm; Scott Spencer

Irina Holmes ; Robert Rahm ; Scott Spencer

Studia Mathematica, Tome 233 (2016), p. 279-291 / Harvested from The Polish Digital Mathematics Library

Résumé

We investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for $μ, λ \in A_{p, q}$ and α/n + 1/q = 1/p, the norm $| | [b, I_{α}] : L^{p} (μ^{p}) \to L^{q} (λ^{q}) | |$ 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.

Publié le : 2016-01-01

Zbl 06602799

EUDML-ID : urn:eudml:doc:286138

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     title = {Commutators with fractional integral operators},
     journal = {Studia Mathematica},
     volume = {233},
     year = {2016},
     pages = {279-291},
     zbl = {06602799},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8419-4-2016}
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Irina Holmes; Robert Rahm; Scott Spencer. Commutators with fractional integral operators. Studia Mathematica, Tome 233 (2016) pp. 279-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8419-4-2016/