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

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Submitted: 2024-12-02; Published: 2024-12-02

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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 C0C0-semigroup via Fourier multipliers in vector-valued Orlicz spaces and establish the relationship between exponential stability and Fourier multipliers in vector-valued Orlicz spaces.