MAXIMAL OPERATOR IN WEIGHTED MORREY SPACES, ASSOCIATED WITH THE LAPLACE-BESSEL DIFFERENTIAL OPERATOR

Abstract

We consider the generalized shift operator, associated with the Laplace-Bessel differential operator. The maximal operator Mγ(B-maximal operator), associated with the generalized shift operator is investigated. At first, we prove that the boundedness of maximal operator weighted Morrey spaces Lp,λ,ω1,γ(Rn k,+) to the spaces Lp,λ,ω2,γ(Rnk,+), where 1 < p < ∞,(ω1, ω2) ∈ Fp,γ(Rnk,+), associated with the Laplace-Bessel differential operator