Matrix weights on compact and non-compact domains

Abstract

We study Muckenhoupt $A_p$ conditions for matrix weights and their connections to related scalar properties for values of p in the range $1\le p<\infty$. Special emphasis is put on the process of diagonalisation of weights and on the role played by the domain of the matrix weight, where it is shown that there are several fundamental structural differences between weights defined on compact and non-compact domains.