# Commutators with fractional integral operators

Irina Holmes; Robert Rahm; Scott Spencer

Studia Mathematica (2016)

- Volume: 233, Issue: 3, page 279-291
- ISSN: 0039-3223

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topIrina Holmes, Robert Rahm, and Scott Spencer. "Commutators with fractional integral operators." Studia Mathematica 233.3 (2016): 279-291. <http://eudml.org/doc/286138>.

@article{IrinaHolmes2016,

abstract = {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 $ν = μλ^\{-1\}$. 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.},

author = {Irina Holmes, Robert Rahm, Scott Spencer},

journal = {Studia Mathematica},

keywords = {fractional integral operator; commutator; weighted inequalities; Bloom BMO},

language = {eng},

number = {3},

pages = {279-291},

title = {Commutators with fractional integral operators},

url = {http://eudml.org/doc/286138},

volume = {233},

year = {2016},

}

TY - JOUR

AU - Irina Holmes

AU - Robert Rahm

AU - Scott Spencer

TI - Commutators with fractional integral operators

JO - Studia Mathematica

PY - 2016

VL - 233

IS - 3

SP - 279

EP - 291

AB - 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 $ν = μλ^{-1}$. 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.

LA - eng

KW - fractional integral operator; commutator; weighted inequalities; Bloom BMO

UR - http://eudml.org/doc/286138

ER -

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