Weighted Estimates for Iterated Commutators of Riesz Potential on Homogeneous Groups

In this paper, we study the two weight commutators theorem of Riesz potential on an arbitrary homogeneous group H of dimension N. Moreover, in accordance with the results in the Euclidean space, we acquire the quantitative weighted bound on homogeneous group.

Some remarks on the sparse dominations for commutators of multi(sub)linear operator

We establish pointwise sparse dominations for the iterated commutators of multi(sub)linear operators satisfying the $W_{q}$ W q condition. As consequences, we present some quantitative weighted estimates for the commutators. In addition, we also obtain the Fefferman–Stein inequality, the Coifman–Fefferman inequality, and the local decay estimates regarding the iterated commutators.

Variation and oscillation inequalities for commutators in two-weight setting

This paper studies the two-weight estimates of variation and oscillation operators for commutators of singular integrals with weighted {\mathrm{BMO}} functions. A new characterization of weighted {\mathrm{BMO}} spaces via the boundedness of variation and oscillation operators for the iterated commutators of Calderón–Zygmund singular integrals in the two-weight setting is given.