Abstract
Let \(1<r<\infty\) and \(T_{r}^{*}\) be a maximal singular integral operator whose kernel satisfies a generalized \(L^{r}\) -Hörmander condition. In this paper, we prove the boundedness of maximal singular integral operator \(T_{r}^{*}\) on weighted Lebesgue spaces. From this and combining with the extrapolation method on the ball Banach function spaces, we further deduce the boundedness of maximal singular integral operator \(T_{r}^{*}\) on ball Banach function spaces. Finally, we apply the boundedness of maximal singular integral operator \(T_{r}^{*}\) on ball Banach function spaces to two concrete examples of ball Banach function spaces, namely, variable Lebesgue spaces and mixed-norm Lebesgue spaces.
