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

Alexei Karlovich; Eugene Shargorodsky

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 4, page 1199-1209
  • ISSN: 0011-4642

Abstract

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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 ' .

How to cite

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Karlovich, Alexei, and Shargorodsky, Eugene. "An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices." Czechoslovak Mathematical Journal 71.4 (2021): 1199-1209. <http://eudml.org/doc/298204>.

@article{Karlovich2021,
abstract = {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 $\Gamma _\{p,w\}^\{\prime \}$.},
author = {Karlovich, Alexei, Shargorodsky, Eugene},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lorentz Gamma space; reflexivity; Boyd indices; Zippin indices},
language = {eng},
number = {4},
pages = {1199-1209},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices},
url = {http://eudml.org/doc/298204},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Karlovich, Alexei
AU - Shargorodsky, Eugene
TI - An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 1199
EP - 1209
AB - 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 $\Gamma _{p,w}^{\prime }$.
LA - eng
KW - Lorentz Gamma space; reflexivity; Boyd indices; Zippin indices
UR - http://eudml.org/doc/298204
ER -

References

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  8. Maligranda, L., Indices and interpolation, Diss. Math. 234 (1985), 1-49. (1985) Zbl0566.46038MR0820076
  9. Pick, L., Kufner, A., John, O., Fučík, S., 10.1515/9783110250428, De Gruyter Series in Nonlinear Analysis and Applications 14. Walter de Gruyter, Berlin (2013). (2013) Zbl1275.46002MR3024912DOI10.1515/9783110250428
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