We deduce continuity properties of classes of Fourier multipliers, pseudo-differential and Fourier integral operators when acting on Orlicz spaces. Especially we show classical results like H{\"o}rmander's improvement of Mihlin's Fourier multiplier theorem are extendable to the framework of Orlicz spaces. We also show how some properties of the Young functions $\Phi$ of the Orlicz spaces are linked to properties of certain Lebesgue exponents $p_\Phi$ and $q_\Phi$ emerged from $\Phi$.

Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents / Bonino, Matteo; Coriasco, Sandro; Petersson, Albin; Toft, Joachim. - (2023).

Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents

Matteo Bonino;
2023

Abstract

We deduce continuity properties of classes of Fourier multipliers, pseudo-differential and Fourier integral operators when acting on Orlicz spaces. Especially we show classical results like H{\"o}rmander's improvement of Mihlin's Fourier multiplier theorem are extendable to the framework of Orlicz spaces. We also show how some properties of the Young functions $\Phi$ of the Orlicz spaces are linked to properties of certain Lebesgue exponents $p_\Phi$ and $q_\Phi$ emerged from $\Phi$.
2023
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2989015