# Duality in a stability problem for some functionals arising in interpolation theory

## TL;DR

This paper demonstrates the existence of near-minimizers for certain distance functionals in interpolation theory that remain stable under singular integral operators, using duality techniques.

## Contribution

It introduces a duality-based approach to establish stability of near-minimizers in interpolation spaces involving $L^ ext{infty}$ and $L^p$.

## Key findings

- Existence of near-minimizers for specific distance functionals.
- Stability of these near-minimizers under singular integral operators.
- Application of duality in interpolation theory.

## Abstract

By using duality, it is shown that there exist near-minimizers for the distance functionals for the couple $(L^\infty, L^p)$, $1<p<\infty$, that are stable under the action of singular integral operators.