Morrey meets Muckenhoupt: A note on Nakai's generalized Morrey spaces and applications

2018/02/11 by Xian Ming Hou, Qingyan Wu, Hou, Xian Ming +5
Mathematics · #42B20 #42B35 #42B99 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.FA #msc:42B20 #msc:42B35 #msc:42B99

paper · pdf · doi:10.48550/arxiv.1802.03743

25 pages

openalex publication_date 2018/02/11 · openalex created_date 2018/02/23 · arxiv created 2018/09/14 · arxiv updated 2018/09/17 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to extend Nakai's generalized Morrey spaces to a wider function class, the one-sided Muckenhoupt weighted case. Morrey matching Muckenhoupt enables us to study the weak and strong type boundedness of one-sided sublinear operators satisfying certain size conditions on the one-sided weighted Morrey spaces. We also establish one-sided Fefferman-Stein inequalities on one-sided weighted Morrey spaces in this paper. Meanwhile, the boundedness and compactness of Riemann-Liouville integral operators on locally one-sided weighted Morrey space are considered. As applications, we establish the existence and uniqueness of solutions to a Cauchy type problem associated with fractional differential equations.

Citations

• On the solutions of quasi-linear elliptic partial differential equations

Related

• Muckenhoupt-type conditions on weighted Morrey spaces
• The boundedness of operators in Muckenhoupt weighted Morrey spaces via extrapolation techniques and duality
• Embeddings of Weighted Morrey Spaces
• Boundedness of the Hardy-Littlewood Maximal Operator, Fractional Integral Operators, and Calderon-Zygmund Operators on Generalized Weighted Morrey Spaces
• Multilinear singular and fractional integral operators on weighted Morrey spaces