Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces

Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces

Let X,d,μ be a nonhomogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. In this setting, the author proves that parameter θ-type Marcinkiewicz integral Mθρ is bounded on the weighted generalized Morrey space Lp,ϕ,τω for p∈1,∞. F...

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Main Author: Guanghui Lu
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/4532312
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spelling doaj-c8ae2e31d3ba41ab9f54ee7fd82b13e22020-12-28T01:30:09ZengHindawi LimitedJournal of Function Spaces2314-88882020-01-01202010.1155/2020/4532312Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey SpacesGuanghui Lu0College of Mathematics and StatisticsLet X,d,μ be a nonhomogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. In this setting, the author proves that parameter θ-type Marcinkiewicz integral Mθρ is bounded on the weighted generalized Morrey space Lp,ϕ,τω for p∈1,∞. Furthermore, the boudedness of Mθρ on weak weighted generalized Morrey space WLp,ϕ,τω is also obtained.http://dx.doi.org/10.1155/2020/4532312
collection DOAJ
language English
format Article
sources DOAJ
author Guanghui Lu
spellingShingle Guanghui Lu
Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces
Journal of Function Spaces
author_facet Guanghui Lu
author_sort Guanghui Lu
title Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces
title_short Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces
title_full Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces
title_fullStr Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces
title_full_unstemmed Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces
title_sort parameter θ-type marcinkiewicz integral on nonhomogeneous weighted generalized morrey spaces
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8888
publishDate 2020-01-01
description Let X,d,μ be a nonhomogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. In this setting, the author proves that parameter θ-type Marcinkiewicz integral Mθρ is bounded on the weighted generalized Morrey space Lp,ϕ,τω for p∈1,∞. Furthermore, the boudedness of Mθρ on weak weighted generalized Morrey space WLp,ϕ,τω is also obtained.
url http://dx.doi.org/10.1155/2020/4532312
work_keys_str_mv AT guanghuilu parameterthtypemarcinkiewiczintegralonnonhomogeneousweightedgeneralizedmorreyspaces
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