We study matrix weights defined on the multivariate torus Td. Sufficient conditions for a matrix weight to be in the Muckenhoupt A2-class are studied, and two such sufficiency results obtained by S. Bloom for d= 1 are generalized to the multivariate setting. As an application, an A2-decomposition property is introduced for matrix weights and a BMO distance theorem for matrix weights is considered.
- Garnett–Jones distance theorem
- Matrix weight
- Muckenhoupt condition
- Weighted BMO