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Mat. Sb., 2019, Volume 210, Number 2, Pages 115–142 (Mi msb9061)  

Tauberian class estimates for vector-valued distributions

S. Pilipovića, J. Vindasb

a Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia
b Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

Abstract: We study Tauberian properties of regularizing transforms of vector-valued tempered distributions. The transforms have the form $M^\mathbf f_\varphi(x,y)=(\mathbf f\ast\varphi_y)(x)$, where the kernel $\varphi$ is a test function and $\varphi_y(\cdot)=y^{-n}\varphi(\cdot/y)$. We investigate conditions which ensure that a distribution that a priori takes values in a locally convex space actually takes values in a narrower Banach space. Our goal is to characterize spaces of Banach-space-valued tempered distributions in terms of so-called class estimates for the transform $M^\mathbf f_\varphi(x,y)$. Our results generalize and improve earlier Tauberian theorems due to Drozhzhinov and Zav'yalov. Special attention is paid to finding the optimal class of kernels $\varphi$ for which these Tauberian results hold.
Bibliography: 24 titles.

Keywords: regularizing transforms, class estimates, Tauberian theorems, vector-valued distributions, wavelet transform.

Funding Agency Grant Number
Ministry of Education, Science and Technical Development of Serbia 174024
Ghent University BOF-grant 01N01014
S. Pilipović's research was carried out with the support of the Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja Republike Srbije (grant 174024). J. Vindas's research was carried out with the support of Universiteit Gent (BOF-grant 01N01014).


DOI: https://doi.org/10.4213/sm9061

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English version:
Sbornik: Mathematics, 2019, 210:2, 272–296

Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: Primary 40E05, 46F05; Secondary 46F12
Received: 05.01.2018

Citation: S. Pilipović, J. Vindas, “Tauberian class estimates for vector-valued distributions”, Mat. Sb., 210:2 (2019), 115–142; Sb. Math., 210:2 (2019), 272–296

Citation in format AMSBIB
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