Approximation in Morrey spaces

TL;DR

This paper introduces a new subspace within Morrey spaces that can be approximated by smooth functions, describes its closure explicitly, and generalizes embeddings into weighted Lebesgue spaces.

Contribution

It presents a novel subspace of Morrey spaces with approximation properties and extends known embeddings into weighted Lebesgue spaces.

Findings

Defined a new subspace of Morrey spaces with smooth approximations

Explicitly characterized the closure of smooth functions in Morrey spaces

Generalized embeddings of Morrey spaces into weighted Lebesgue spaces

Abstract

A new subspace of Morrey spaces whose elements can be approximated by infinitely differentiable compactly supported functions is introduced. Consequently, we give an explicit description of the closure of the set of such functions in Morrey spaces. A generalization of known embeddings of Morrey spaces into weighted Lesbesgue spaces is also obtained.