Weighted Hardy operators in local generalized Orlicz-Morrey spaces - Aykol, C.; Azizova, Z.O.; Hasanov, J.J. (Carpathian Mathematical Publications, 2021)
In this paper, we find sufficient conditions on general Young functions $(Φ, Ψ)$ and the functions $(φ_1,φ_2)$ ensuring that the weighted Hardy operators $A_ω^α$ and ${\mathcal A}_ω^α$ are of strong type from a local generalized Orlicz-Morrey space $M^{0,\,loc}_{Φ,\,φ_1}(\mathbb R^n)$ into another local generalized Orlicz-Morrey space $M^{0,\,loc}_{Ψ,\,φ_2}(\mathbb R^n)$. We also obtain the boundedness of the commutators of $A_ω^α$ and ${\mathcal A}_ω^α$ from $M^{0,\,loc}_{Φ,\,φ_1}(\mathbb R^n)$ to $M^{0,\,loc}_{Ψ,\,φ_2}(\mathbb R^n)$.