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We study weigted altered Ces\`aro space Ch$_{\infty,w}(I)$, which isnon-ideal enlargement of the usual Ces\`aro space. We prove the connection ofthe space with one weighted Sobolev space of first order on real line and givecharacterization of associate spaces for the space.

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