Composition of fractional Orlicz maximal operators and A1-weights on spaces of homogeneous type

Authors
Bernardis, Ana Lucia; Pradolini, Gladis Guadalupe; Lorente, María; Riveros, Maria Silvina
Publication Year
2010
Language
English
Format
article
Status
Published version
Description
For a Young function Θ with 0 ≤ α < 1, let Mα,Θ be the fractional Orlicz maximal operator defined in the context of the spaces of homogeneous type (X, d, μ) by Mα,Θf(x) = supx∈Bμ(B)α{double pipe}f{double pipe}Θ,B, where {double pipe}f{double pipe}Θ,B is the mean Luxemburg norm of f on a ball B. When α = 0 we simply denote it by MΘ. In this paper we prove that if Φ and Ψ are two Young functions, there exists a third Young function Θ such that the composition Mα,Ψ {ring operator} MΦ is pointwise equivalent to Mα,Θ. As a consequence we prove that for some Young functions Θ, if Mα,Θf <∞ a.e. and δ ∈ (0,1) then (Mα,Θf)δ is an A1-weight.
Fil: Bernardis, Ana Lucia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Pradolini, Gladis Guadalupe. Universidad Nacional del Litoral; Argentina
Fil: Lorente, María. Universidad de Málaga; España
Fil: Riveros, Maria Silvina. Universidad Nacional de Córdoba; Argentina
Subject
ORLICZ MAXIMAL FUNCTION
SPACES OF HOMOGENEOUS TYPE
WEIGHTS
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS
Access level
Open access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/75199