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An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices

Alexei KarlovichEugene Shargorodsky — 2021

Czechoslovak Mathematical Journal

We show that for every p ( 1 , ) there exists a weight w such that the Lorentz Gamma space Γ p , w is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space Γ p , w and on its associate space Γ p , w ' .

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