Optimal behavior of weighted Hardy operators on rearrangement-invariant spaces |
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Authors: | Zdeněk Mihula |
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Affiliation: | Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Mathematics, Czech Republic |
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Abstract: | The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied. Emphasis is put on the optimality of the obtained results. First, the optimal rearrangement-invariant function spaces guaranteeing the boundedness of the operators from/to a given rearrangement-invariant function space are described. Second, the optimal rearrangement-invariant function norms being sometimes complicated, the question of whether and how they can be simplified to more manageable expressions is addressed. Next, the relation between optimal rearrangement-invariant function spaces and interpolation spaces is investigated. Last, iterated weighted Hardy-type operators are also studied. |
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Keywords: | iterated operators optimal spaces rearrangement-invariant spaces supremum operators weighted Hardy operators |
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