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Vector-valued Fourier multipliers in $L_p$-spaces with power weights

Volume 247 / 2019

Jan Prüss 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.

Authors

  • Jan PrüssInstitut für Mathematik
    Martin-Luther-Universität Halle-Wittenberg
    Theodor-Lieser-Strasse 5
    D-06120 Halle, Germany
    e-mail

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