Two-weighted inequalities of maximal commutators in the modified Morrey spaces, associated with the Laplace-Bessel differential operator

Abstract

We consider the generalized shift operator, associated with the LaplaceBessel differential operator ∆B =∑ni=1∂2∂x2i+∑ki=1γixi∂∂xi. The maximal commutators Mb,γ, associated with the generalized shift operator are investigated. At first, we prove that the maximal commutators is bounded from the modified Morrey space Lep,λ,φ1,γ(Rnk,+) to Lep,λ,φ1,γ(R n k,+) for all 1 < p < ∞, b ∈ BMOγ(Rnk,+), (φ1, φ2) ∈ Aep,γ(Rnk,+).