The singular integral operator and its commutator on weighted Morrey spaces
By Shohei Nakamura, Yoshihiro Sawano. 2016
49 citations recorded by the source corpus.
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 $$A_q$$Aq-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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4e75a1d7268387eebd56fd14289759aca64802e4
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In Applied Mathematics
- T. Nogayama
- Yoshihiro Sawano
- Dachun Yang
- Wen Yuan
- Ciqiang Zhuo
- Shohei Nakamura
- Long Huang
- Kwok-Pun Ho
In Mathematical Physics
- T. Nogayama
- Yoshihiro Sawano
- Dachun Yang
- Wen Yuan
- Ciqiang Zhuo
- Kwok-Pun Ho
- Shohei Nakamura
- M. Rosenthal
Citations in the corpus
- Boundedness of commutators of fractional integral operators on mixed Morrey spaces (2019, methodology): “Before we obtain the final form of the sharp maximal inequalities in Morrey spaces, we obtain a norm equivalence similar to [33,50].”
- A Thought on Generalized Morrey Spaces (2018, methodology): “One can use martingales to generalize Morrey spaces [80, 84].”