Smoothing Properties of the Friedrichs Operator on $L^p$ spaces

TL;DR

This paper investigates the smoothing effects of the Friedrichs operator on $L^p$ spaces, demonstrating its ability to map functions to higher integrability spaces on smooth pseudoconvex domains.

Contribution

It establishes that the Friedrichs operator maps $A^2( ext{domain})$ to $A^p( ext{domain})$ for some $p>2$, revealing new smoothing properties.

Findings

Friedrichs operator exhibits smoothing in $L^p$ spaces.

Maps $A^2( ext{domain})$ to $A^p( ext{domain})$ for some $p>2$.

Valid on smoothly bounded pseudoconvex domains.

Abstract

We show that the Friedrichs operator exhibits smoothing properties in the $L^p$ scale. In particular we prove that on any smoothly bounded pseudoconvex domain the Friedrichs operator maps $A^2(\Omega)$ to $A^p(\Omega)$ for some $p>2$.