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

Alexei Karlovich; Eugene Shargorodsky

doi:10.21136/CMJ.2021.0355-20

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

Alexei Karlovich, Eugene Shargorodsky

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1199-1209
Number of pages	11
Journal	Czechoslovak Mathematical Journal
Volume	71
Issue number	4
DOIs	https://doi.org/10.21136/CMJ.2021.0355-20
Publication status	Published - Dec 2021

Keywords

42B25
46E30
Boyd indices
Lorentz Gamma space
reflexivity
Zippin indices

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10.21136/CMJ.2021.0355-20

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title = "An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices",

abstract = "We show that for every p ∈ (1, ∞) there exists a weight w such that the Lorentz Gamma space Γp,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 Γp,w and on its associate space Γ'p,w.",

keywords = "42B25, 46E30, Boyd indices, Lorentz Gamma space, reflexivity, Zippin indices",

author = "Alexei Karlovich and Eugene Shargorodsky",

note = "Funding Information: This work was partially supported by the Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UIDB/MAT/00297/2020 (Centro de Matem{\'a}tica e Aplica{\c c}{\~o}es). Acknowledgment ",

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AU - Karlovich, Alexei

AU - Shargorodsky, Eugene

N1 - Funding Information: This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UIDB/MAT/00297/2020 (Centro de Matemática e Aplicações). Acknowledgment

PY - 2021/12

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N2 - We show that for every p ∈ (1, ∞) there exists a weight w such that the Lorentz Gamma space Γp,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 Γp,w and on its associate space Γ'p,w.

AB - We show that for every p ∈ (1, ∞) there exists a weight w such that the Lorentz Gamma space Γp,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 Γp,w and on its associate space Γ'p,w.

KW - 42B25

KW - 46E30

KW - Boyd indices

KW - Lorentz Gamma space

KW - reflexivity

KW - Zippin indices

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SN - 0011-4642

VL - 71

SP - 1199

EP - 1209

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

IS - 4

ER -

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

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