Parameter θ-Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces. (16th December 2020)

• Record Type: Journal Article
• Authors: Lu, Guanghui
• Other Names: Sawano Yoshihiro Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-12-16
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/4532312
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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 M θ ρ is bounded on the weighted generalized Morrey space L p, ϕ, τ ω for p ∈ 1, ∞ . Furthermore, the boudedness of M θ ρ on weak weighted generalized Morrey space W L p, ϕ, τ ω is also obtained.