A generalized weighted Hardy-Cesàro operator, and its commutator on weighted L^p and BMO spaces

2012/08/26 by Nguyen Minh Chuong, Chuong, Nguyen Minh, Duy-Hung Ha +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1208.5242

openalex publication_date 2012/08/26 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a new weighted Hardy-Cesàro operator defined by U_ψ,sf(x)=∫₀¹ f(s(t)⋅ x) ψ(t)dt, which is associated to the parameter curve s(t,x)=s(t)x. Under certain conditions on s(t) and on an absolutely homogeneous weight function ω, we characterize the weight function ψ such that U_ψ,s is bounded on L^p(ω), BMO(ω). The corresponding operator norms are worked out too. These results extend the ones of Jie Xiao \citexiao. We also give a sufficient and a necessary condition on the weight function ψ, which ensure the boundedness of the commutators of operator U_ψ,s on L^p(ω) with symbols in BMO(ω).

Related

• Generalized Hardy-Cesàro operators between weighted spaces
• Multilinear Hardy-Cesàro Operator and Commutator on the product of Morrey-Herz spaces
• New weighted multilinear operators and commutators of Hardy-Cesàro type
• Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms
• Cesaro operators on the Hardy spaces of the half-plane