Embeddings of Weighted Morrey Spaces

TL;DR

This thesis explores the properties of weighted Morrey spaces, extending classical results by incorporating Muckenhoupt weights and analyzing the boundedness of the Hardy-Littlewood maximal operator within these spaces.

Contribution

It introduces new insights into weighted Morrey spaces, including their properties, embeddings, and the boundedness of key operators, expanding the understanding of these function spaces.

Findings

Boundedness of Hardy-Littlewood maximal operator on weighted Morrey spaces

Characterization of embeddings between weighted Morrey spaces with specific weights

Extension of classical Morrey space properties to weighted settings

Abstract

In this master thesis we recall already established definitions and basic properties of classical Morrey spaces in an attempt to expand known facts to their weighted counterparts. To do so, we will recall properties of Muckenhoupt weights, which we will use to derive further properties of weighted Morrey spaces. We will also show the boundedness of the Hardy-Littlewood maximal operator on weighted Morrey spaces. Throughout this thesis we will have a look at example weights and show in which case Morrey spaces equipped with these weights are embedded in each other.