Two-weight norm inequalities for the higher-order commutators of fractional integral operators. (English) Zbl 1373.42020

Niu, Caiyin; Zhang, Xiaojin

Adv. Oper. Theory 2, No. 3, 201-214 (2017).

Summary: In this paper, we obtain several sufficient conditions such that the higher-order commutators \(I_{\alpha,b}^m\) generated by \(I_\alpha\) and \(b\in \mathrm{BMO}(\mathbb{R}^n)\) is bounded from \(L^p(v)\) to \(L^q(u)\), where \(\frac{1}{q}=\frac{1}{p}-\frac{\alpha}{n}\) and \(0<\alpha<n\).

MSC:

42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B35	Function spaces arising in harmonic analysis

Keywords:

fractional integrals; BMO; higher-order commutators; two-weight