TY - JOUR
T1 - A necessary condition for the boundedness of the maximal operator on Lp(·) over reverse doubling spaces of homogeneous type
AU - Karlovych, O.
AU - Shalukhina, A.
N1 - info:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017%2F2018) - Financiamento Base/UIDB%2F00297%2F2020/PT#
info:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017%2F2018) - Financiamento Programático/UIDP%2F00297%2F2020/PT#
Funding Information:
Open access funding provided by FCT |FCCN (b-on).
Publisher Copyright:
© The Author(s) 2024.
PY - 2024/10/2
Y1 - 2024/10/2
N2 - Let (X,d,μ) be a space of homogeneous type and p(·):X→[1,∞] be a variable exponent. We show that if the measure μ is Borel-semiregular and reverse doubling, then the condition essinfx∈Xp(x)>1 is necessary for the boundedness of the Hardy–Littlewood maximal operator M on the variable Lebesgue space Lp(·)(X,d,μ).
AB - Let (X,d,μ) be a space of homogeneous type and p(·):X→[1,∞] be a variable exponent. We show that if the measure μ is Borel-semiregular and reverse doubling, then the condition essinfx∈Xp(x)>1 is necessary for the boundedness of the Hardy–Littlewood maximal operator M on the variable Lebesgue space Lp(·)(X,d,μ).
KW - 28C15
KW - 42B25
KW - 46E30
KW - Borel-semiregular measure
KW - reverse doubling condition
KW - space of homogeneous type
KW - The Hardy–Littlewood maximal operator
KW - variable Lebesgue space
UR - http://www.scopus.com/inward/record.url?scp=85205425171&partnerID=8YFLogxK
U2 - 10.1007/s10476-024-00053-6
DO - 10.1007/s10476-024-00053-6
M3 - Article
AN - SCOPUS:85205425171
SN - 0133-3852
JO - Analysis Mathematica
JF - Analysis Mathematica
ER -