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

TL;DR

This paper investigates the structure of weighted altered Cesàro spaces, establishing their relationship with weighted Sobolev spaces and characterizing their associate spaces, thus advancing understanding of their functional properties.

Contribution

It introduces the weighted altered Cesàro space, links it to weighted Sobolev spaces, and characterizes its associate spaces, providing new insights into their structure.

Findings

Connected the space with weighted Sobolev spaces of first order

Provided a characterization of the associate spaces

Enhanced understanding of the space's functional properties

Abstract

We study weigted altered Ces\`aro space Ch$_{\infty,w}(I)$, which is non-ideal enlargement of the usual Ces\`aro 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.