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arXiv · 2309.15229

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

Matteo Bonino·Sandro Coriasco·Albin Petersson·Joachim Toft
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Abstract

We deduce continuity and (global) wave-front properties of classes of Fourier multipliers, pseudo-differential, and Fourier integral operators when acting on Orlicz spaces, or more generally, on Orlicz-Sobolev type spaces. In particular, we extend H{\"o}rmander's improvement of Mihlin's Fourier multiplier theorem to the framework of Orlicz spaces. We also show how Young functions $\Phi$ of the Orlicz spaces are linked to properties of certain Lebesgue exponents $p_\Phi$ and $q_\Phi$ emerged from $\Phi$.

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Matteo Bonino, Sandro Coriasco, Albin Petersson, Joachim Toft. 2023-09-26. Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents. https://arxiv.org/abs/2309.15229

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