Operator-Valued Fourier Multipliers on Vector-Valued Orlicz Spaces and their Applications

Jingshi Xu; Yang Mei

doi:10.52737/18291163-2024.16.11-1-19

Authors

Jingshi Xu Guilin University of Electronic Technology
Yang Mei Guilin University of Electronic Technology

DOI:

https://doi.org/10.52737/18291163-2024.16.11-1-19

Keywords:

Fourier Multiplier, Orlicz Space, Operator-Valued, Semigroup

Abstract

In this paper, we extend the operator-valued Fourier multiplier theorem on Lebesgue spaces to vector-valued Orlicz spaces. Then we characterize the growth bound of a $C_0$-semigroup via Fourier multipliers in vector-valued Orlicz spaces and establish the relationship between exponential stability and Fourier multipliers in vector-valued Orlicz spaces.

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