Commutators with fractional integral operators

• Autorzy: Irina Holmes , Robert Rahm , Scott Spencer
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42A61: Probabilistic methods
• 42B25: Maximal functions, Littlewood-Paley theory
• 42A50: Conjugate functions, conjugate series, singular integrals
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 42A05: Trigonometric polynomials, inequalities, extremal problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 233
• Numer: 3
• Strony: 279-291

Daty

wydano

2016

Twórcy

autor

Irina Holmes

• School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, U.S.A.

autor

Robert Rahm

• School of Mathematics, Washington University in St. Louis, One Brookings Drive, St. Louis, MO 63130, U.S.A.

autor

Scott Spencer

• School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, U.S.A.

Identyfikatory

DOI

10.4064/sm8419-4-2016