Operator-Valued Fourier Multipliers on Vector-Valued Orlicz Spaces and their Applications - Xu, Jingshi; Mei, Yang (Armenian Journal of Mathematics, 2024)
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.
Keywords: Fourier Multiplier; Orlicz Space; Operator-Valued; Semigroup