Vector-valued Fourier multipliers in $L_p$-spaces with power weights
Volume 247 / 2019
Studia Mathematica 247 (2019), 155-173
MSC: 35K65, 42A45.
DOI: 10.4064/sm170307-19-10
Published online: 22 November 2018
Abstract
The vector-valued Fourier multiplier theorem due to L. Weis (2001) for $L_p({\mathbb R};X)$, $1 \lt p \lt \infty $, $X$ of class UMD, is extended in an elementary way to the weighted spaces $L_{p,\mu }({\mathbb R};X)$ with $1/p \lt \mu \lt 1+1/p$. The result is applied to Volterra operators and fractional evolution equations in such vector-valued weighted spaces.
