On the associated spaces for the weighted altered Cesàro space Ch${}_{\mathrm{\infty },w}(I)$

We study weigted altered Cesàro space Ch${}_{\mathrm{\infty },w}(I)$, which is non-ideal enlargement of the usual Cesàro space. We prove the connection of the space with one weighted Sobolev space of first order on real line and give characterization of associate spaces for the space.