Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces
The spaces of pointwise multipliers on Morrey spaces are described in terms of Morrey spaces, their preduals, and vector-valued Morrey spaces introduced by Ho. This paper covers weak Morrey spaces as well. The result in the present paper completes the characterization of the earlier works of the fir...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2754 |
| _version_ | 1797512109721911296 |
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| author | Eiichi Nakai Yoshihiro Sawano |
| author_facet | Eiichi Nakai Yoshihiro Sawano |
| author_sort | Eiichi Nakai |
| collection | DOAJ |
| description | The spaces of pointwise multipliers on Morrey spaces are described in terms of Morrey spaces, their preduals, and vector-valued Morrey spaces introduced by Ho. This paper covers weak Morrey spaces as well. The result in the present paper completes the characterization of the earlier works of the first author’s papers written in 1997 and 2000, as well as Lemarié-Rieusset’s 2013 paper. As a corollary, the main result in the present paper shows that different quasi-Banach lattices can create the same vector-valued Morrey spaces. The goal of the present paper is to provide a complete picture of the pointwise multiplier spaces. |
| first_indexed | 2024-03-10T05:57:14Z |
| format | Article |
| id | doaj.art-d7ac321079f441e990267e926d6d6b5b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:57:14Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d7ac321079f441e990267e926d6d6b5b2023-11-22T21:18:22ZengMDPI AGMathematics2227-73902021-10-01921275410.3390/math9212754Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey SpacesEiichi Nakai0Yoshihiro Sawano1Department of Mathematics, Ibaraki University, Mito 310-8512, Ibaraki, JapanDepartment of Mathematics, Chuo University, 1-13-27, Kasuga 112-8551, Bunkyo, JapanThe spaces of pointwise multipliers on Morrey spaces are described in terms of Morrey spaces, their preduals, and vector-valued Morrey spaces introduced by Ho. This paper covers weak Morrey spaces as well. The result in the present paper completes the characterization of the earlier works of the first author’s papers written in 1997 and 2000, as well as Lemarié-Rieusset’s 2013 paper. As a corollary, the main result in the present paper shows that different quasi-Banach lattices can create the same vector-valued Morrey spaces. The goal of the present paper is to provide a complete picture of the pointwise multiplier spaces.https://www.mdpi.com/2227-7390/9/21/2754pointwise multipliersMorrey spacesblock spacesconvexification |
| spellingShingle | Eiichi Nakai Yoshihiro Sawano Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces Mathematics pointwise multipliers Morrey spaces block spaces convexification |
| title | Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces |
| title_full | Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces |
| title_fullStr | Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces |
| title_full_unstemmed | Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces |
| title_short | Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces |
| title_sort | spaces of pointwise multipliers on morrey spaces and weak morrey spaces |
| topic | pointwise multipliers Morrey spaces block spaces convexification |
| url | https://www.mdpi.com/2227-7390/9/21/2754 |
| work_keys_str_mv | AT eiichinakai spacesofpointwisemultipliersonmorreyspacesandweakmorreyspaces AT yoshihirosawano spacesofpointwisemultipliersonmorreyspacesandweakmorreyspaces |