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arXiv · 2307.02217

Paley inequality for the Weyl transform and its applications

Ritika Singhal·N. Shravan Kumar
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Abstract

In this paper, we prove several versions of the classical Paley inequality for the Weyl transform. As an application, we discuss $L^p$-$L^q$ boundedness of the Weyl multipliers and prove a version of the H\"ormander's multiplier theorem. We also prove Hardy-Littlewood inequality. Finally, we study vector-valued versions of these inequalities. In particular, we consider the inequalities of Paley, Hausdorff-Young, and Hardy-Littlewood and their relations.

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BibTeXRIS

Ritika Singhal, N. Shravan Kumar. 2023-07-05. Paley inequality for the Weyl transform and its applications. https://arxiv.org/abs/2307.02217

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