TY - JOUR
T1 - An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices
AU - Shargorodsky, Eugene
AU - Karlovich, Alexei
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
Publisher Copyright:
© 2021, Institute of Mathematics, Czech Academy of Sciences.
PY - 2021/11/16
Y1 - 2021/11/16
N2 - 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.
AB - 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.
KW - Lorentz Gamma space, reflexivity, Boyd indices, Zippin indices.
UR - http://www.scopus.com/inward/record.url?scp=85119044310&partnerID=8YFLogxK
U2 - 10.21136/CMJ.2021.0355-20
DO - 10.21136/CMJ.2021.0355-20
M3 - Article
SN - 0011-4642
VL - 71
SP - 1199
EP - 1209
JO - CZECHOSLOVAK MATHEMATICAL JOURNAL
JF - CZECHOSLOVAK MATHEMATICAL JOURNAL
IS - 4
ER -