Projection operators on matrix weighted LpL^p and a simple sufficient Muckenhoupt condition

Abstract

Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted LpL^p-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient conditions, which are straightforward to verify, are obtained that ensure that a given matrix weight is contained in the Muckenhoupt matrix ApA_p class. Applications to singular integral operators with product kernels are considered

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