# Conjugates of integral functionals on continuous functions

## TL;DR

This paper establishes necessary and sufficient conditions for the dual representation of convex integral functionals on the space of continuous functions, extending Rockafellar's foundational work from 1971.

## Contribution

It provides a complete characterization of dual representations for convex integral functionals on continuous functions, advancing the theoretical understanding in convex analysis.

## Key findings

- Characterization of dual representations for convex integral functionals.
- Extension of Rockafellar's 1971 results to broader conditions.
- Theoretical conditions for duality in continuous function spaces.

## Abstract

This article gives necessary and sufficient conditions for the dual representation of Rockafellar in (Integrals which are convex functionals. II, Pacific J. Math., 39:439--469, 1971) for integral functionals on the space of continuous functions.