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arXiv · 2505.06112

Weighted function spaces: convolutors, multipliers, and mollifiers

Lenny Neyt·Yoshihiro Sawano
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Abstract

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.

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Lenny Neyt, Yoshihiro Sawano. 2025-10-30. Weighted function spaces: convolutors, multipliers, and mollifiers. https://arxiv.org/abs/2505.06112

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