Paley inequality for the Weyl transform and its applications

2023/07/05 by Ritika Singhal, Singhal, Ritika, N. Shravan Kumar +1
Mathematics · #43A15 #43A25 #43A32 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2307.02217

openalex publication_date 2023/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Hörmander'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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