Weighted function spaces: convolutors, multipliers, and mollifiers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915585801060352 |
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| author | Neyt, Lenny Sawano, Yoshihiro |
| author_facet | Neyt, Lenny Sawano, Yoshihiro |
| contents | We study smooth function spaces of Gelfand-Shilov type, with global behavior governed through a translation-invariant Banach function space and localized via a weight function system. We clarify the roles of the translation-invariant Banach function space, convolution, and pointwise multiplication in connection with the weight function system. Our primary goal is to characterize these function spaces-as well as the corresponding convolutor and multiplier spaces-through mollification. For this purpose, we introduce the moment-wise decomposition factorization property for pairs of compactly supported smooth functions, and establish complete characterizations in terms of mollifications with these windows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted function spaces: convolutors, multipliers, and mollifiers Neyt, Lenny Sawano, Yoshihiro Functional Analysis 46E10, 46F05, 46H25 We study smooth function spaces of Gelfand-Shilov type, with global behavior governed through a translation-invariant Banach function space and localized via a weight function system. We clarify the roles of the translation-invariant Banach function space, convolution, and pointwise multiplication in connection with the weight function system. Our primary goal is to characterize these function spaces-as well as the corresponding convolutor and multiplier spaces-through mollification. For this purpose, we introduce the moment-wise decomposition factorization property for pairs of compactly supported smooth functions, and establish complete characterizations in terms of mollifications with these windows. |
| title | Weighted function spaces: convolutors, multipliers, and mollifiers |
| topic | Functional Analysis 46E10, 46F05, 46H25 |
| url | https://arxiv.org/abs/2505.06112 |