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The reverse H\"older inequality for mathcal{A}_(p(cdot)) weights with applications to matrix weights
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The reverse H\"older inequality for mathcal{A}_(p(cdot)) weights with applications to matrix weights
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In this paper we prove a reverse H\"{o}lder inequality for the variable exponent Muckenhoupt weights $\mathcal{A}_{p(\cdot)}$, introduced by the first author, Fiorenza, and Neugeabauer. All of our estimates are quantitative, showing the dependence of the exponent function on the $\mathcal{A}_{p(\cdot)}$ characteristic. As an application, we use the reverse H\"{o}lder inequality to prove that the matrix $\mathcal{A}_{p(\cdot)}$ weights, introduced in our previous paper, have both a right and left-openness property. This result is new even in the scalar case.
Forward citations
Cited by 2 Pith papers
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On off-diagonal operators in matrix-weighted spaces
Off-diagonal convex body domination yields improved matrix-weighted bounds for fractional integrals, commutators, and Sobolev inequalities.
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Variable Muckenhoupt $A_\infty$ Weights
Defines variable A_{p(·),∞} weights and shows they are equivalent to the reverse Hölder condition in variable Lebesgue spaces, with matrix versions and dimension estimates for reducing operators.
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