Boundedness of some operators on grand generalized weighted Morrey spaces on RD-spaces

2022/10/04 by He, Suixin, Tao, Shuangping
#42B20(Primary) #42B35(Secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2210.01468

Abstract

The aim of this paper is to obtain the boundedness of some operator on grand generalized weighted Morrey spaces L^p),ϕ_φ(ω) over RD-spaces. Under assumption that functions φ and ϕ satisfy certain conditions, the authors prove that Hardy-Littlewood maximal operator and θ-type Calderón-Zygmund operator are bounded on grand generalized weighted Morrey spaces L^p),ϕ_φ(ω). Moreover, the boundedness of commutator [b,T_θ] which is generated by θ-type Calderón-Zygmund operator T_θ and b\inBMO(μ) on spaces L^p),ϕ_φ(ω) is also established. The results regarding the grand generalized weighted Morrey spaces is new even for domains of Euclidean spaces.

Related

• Boundedness of the Hardy-Littlewood Maximal Operator, Fractional Integral Operators, and Calderon-Zygmund Operators on Generalized Weighted Morrey Spaces
• Norm inequalities in generalized Morrey spaces
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• Boundedness of θ-type Calderón--Zygmund operators and commutators in the generalized weighted Morrey spaces
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