EN
We consider the axisymmetric Navier-Stokes equations with non-zero swirl component. By invoking the Hardy-Sobolev interpolation inequality, Hardy inequality and the theory of $*A_{β}$ (1 < β < ∞) weights, we establish regularity criteria involving $u^{r}$, $ω^{z}$ or $ω^{θ}$ in some weighted Lebesgue spaces. This improves many previous results.