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A new characterization of the Muckenhoupt $A_p$ weights through an extension of the Lorentz-Shimogaki Theorem
Given any quasi-Banach function space X over R n , an index α x is defined that coincides with the upper Boyd index α x when the space X is rearrangement-invariant. This new index is defined by means of the local maximal operator m λ f. It is shown then …