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Fourier Multipliers on Quasi-Banach Orlicz Spaces and Orlicz Modulation Spaces

Petersson, Albin
arXiv (All) · Papers
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functional-analysis
We find that if a Fourier multiplier is continuous from $L^{Φ_1}$ to $L^{Φ_2}$, then it is also continuous from $M^{Φ_1,Ψ}$ to $M^{Φ_2,Ψ}$, where $Φ_1,Φ_2,Ψ$ are quasi-Young functions and $Φ_1$ fulfills the $Δ_2$-condition. This result is applied to show that Mihlin's Fourier multiplier theorem and
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