Inverse Volume Inequalities for Matrix Weights

@inproceedings{BownikInverseVI,
  title={Inverse Volume Inequalities for Matrix Weights},
  author={Marcin Bownik}
}
For weights in the matricial Muckenhoupt classes we investigate a number of properties analogous to properties which hold in the scalar Muckenhoupt classes. In contrast to the scalar case we exhibit for each p, 1 < p <∞, a matrix weight W ∈Ap,q \ ⋃ p′<pAp′,q′ . We also give a necessary and sufficient condition on W in Ap,q, a “reverse inverse volume inequality”, to ensure that W is inAp′,q′ for some p′ < p. 

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