Two results related to elliptic and parabolic equations. Case of Morrey spaces

TL;DR

This paper provides a concise proof of a theorem by Adams and establishes a trace-class theorem for parabolic Morrey spaces, advancing the understanding of elliptic and parabolic equations in these function spaces.

Contribution

It introduces a new short proof of Adams's theorem and a trace-class theorem specific to parabolic Morrey spaces, offering novel insights into these mathematical structures.

Findings

A simplified proof of Adams's theorem.

A new $t$-trace-class theorem for parabolic Morrey spaces.

Enhanced understanding of elliptic and parabolic equations in Morrey spaces.

Abstract

The paper presents a new short proof of one of Adams's theorems and a $t$-trace-class theorem for parabolic Morrey spaces.