Tauberian class estimates for vector-valued distributions
Sbornik. Mathematics, Tome 210 (2019) no. 2, pp. 272-296
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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.
@article{SM_2019_210_2_a4,
author = {S. Pilipovi\'c and J. Vindas},
title = {Tauberian class estimates for vector-valued distributions},
journal = {Sbornik. Mathematics},
pages = {272--296},
publisher = {mathdoc},
volume = {210},
number = {2},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2019_210_2_a4/}
}
S. Pilipović; J. Vindas. Tauberian class estimates for vector-valued distributions. Sbornik. Mathematics, Tome 210 (2019) no. 2, pp. 272-296. http://geodesic.mathdoc.fr/item/SM_2019_210_2_a4/