Improved Caffarelli-Kohn-Nirenberg and trace inequalities for radial functions

TL;DR

This paper demonstrates that restricting to radially symmetric functions extends the range of power weights for Caffarelli-Kohn-Nirenberg and trace inequalities, leading to improved inequalities in these settings.

Contribution

It establishes enhanced versions of Caffarelli-Kohn-Nirenberg and trace inequalities specifically for radially symmetric functions, broadening their applicability.

Findings

Extended range of power weights for inequalities

Improved inequalities for radial functions

Potential applications in PDE analysis

Abstract

We show that Caffarelli-Kohn-Nirenberg first order interpolation inequalities as well as weighted trace inequalities in $\mathbb{R}^n \times \mathbb{R}_+$ admit a better range of power weights if we restrict ourselves to the space of radially symmetric functions.