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An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1199-1209 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We show that for every $p\in (1,\infty )$ there exists a weight $w$ such that the Lorentz Gamma space $\Gamma _{p,w}$ 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 $\Gamma _{p,w}$ and on its associate space $\Gamma _{p,w}'$.
We show that for every $p\in (1,\infty )$ there exists a weight $w$ such that the Lorentz Gamma space $\Gamma _{p,w}$ 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 $\Gamma _{p,w}$ and on its associate space $\Gamma _{p,w}'$.
DOI : 10.21136/CMJ.2021.0355-20
Classification : 42B25, 46E30
Keywords: Lorentz Gamma space; reflexivity; Boyd indices; Zippin indices 
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     title = {An example of a reflexive {Lorentz} {Gamma} space with trivial {Boyd} and {Zippin} indices},
     journal = {Czechoslovak Mathematical Journal},
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Karlovich, Alexei; Shargorodsky, Eugene. An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1199-1209. doi: 10.21136/CMJ.2021.0355-20

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