Grand weighted variable Herz-Morrey spaces estimate for some operators - Ming Liu; Binhua Feng (Communications in Analysis and Mechanics)
In this paper, we established the boundedness of higher-order commutators $ I_{β, b}^{m} $ generated by the fractional integral operator with BMO functions on grand weighted variable-exponent Herz-Morrey spaces $ \mathrm{M\dot{K}}_{λ, p(·)}^{α, r), θ}(ω) $. We also obtained the boundedness of the $ m- $order multilinear fractional Hardy operator $ \mathcal{H}_{β, m} $ and its adjoint operator $ \mathcal{H}^{*}_{β, m} $ on weighted variable-exponent Herz-Morrey spaces $ \mathrm{M\dot{K}}_{q, p(·)}^{α, λ}(ω) $.