Sobolev-type theorem for commutators of Hardy operators in grand Herz spaces - Sultan, Babar; Sultan, Mehvish (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 517.5The higher-order commutators of fractional Hardy-type operators of variable order $ζ(z)$ are shown to be bounded from the grand variable Herz spaces ${\dot{K} ^{a(·), u),θ}_{ p(·)}(\mathbb{R}^n)}$ into the weighted space ${\dot{K} ^{a(·), u),θ}_{ρ, q(·)}(\mathbb{R}^n)},$ where $ρ=(1+|z_1|)^{-λ}$ and $\displaystyle {1 \over q(z)}={1 \over p(z)}-{ζ (z) \over n}$ if $p(z)$ is not necessarily constant at infinity.