The singular integral operator and its commutator on weighted Morrey spaces

2016/06/03 by Shohei Nakamura, Yoshihiro Sawano, Nakamura, Shohei +1
Mathematics · #42B20 (Primary) #42B25 #46E30 (Secondary) #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1606.00971

openalex publication_date 2016/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the A_q-theory by Muckenhoupt and Wheeden does not suffice. We also discuss the boundedness of the commutators. The difference between the maximal operator and the singular integral operators will be clarified. Further, the property of the sharp maximal operator is investigated.

Related

• Maximal operators and singular integrals on the weighted Lorentz and Morrey spaces
• Some estimates for commutators of Calderón-Zygmund operators on the weighted Morrey spaces
• Boundedness of oscillatory integral operators and their commutators on weighted Morrey spaces
• On the boundedness of singular integrals in Morrey spaces and its preduals
• Commutators of Maximal Operators on Weighted Morrey Spaces