韦尔变换的帕利不等式及其应用

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-03-25 DOI:10.1515/forum-2023-0302

Ritika Singhal, N. Shravan Kumar

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引用次数: 0

摘要

在本文中，我们证明了韦尔变换经典帕利不等式的几个版本。至于一些应用，我们证明了赫曼德乘数定理的一个版本，讨论了韦尔乘数的 L p {L^{p}} L q {L^{q}} 有界性，并证明了哈代-利特尔伍德不等式。 - L q {L^{q}} 的有界性，并证明了哈代-利特尔伍德不等式。我们还考虑了 Paley、Hausdorff-Young 和 Hardy-Littlewood 不等式的向量值版本及其关系。最后，我们还证明了韦尔变换的皮特不等式。

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Paley inequality for the Weyl transform and its applications

In this paper, we prove several versions of the classical Paley inequality for the Weyl transform. As for some applications, we prove a version of the Hörmander’s multiplier theorem to discuss L p

{L^{p}}

- L q

{L^{q}}

boundedness of the Weyl multipliers and prove the Hardy–Littlewood inequality. We also consider the vector-valued version of the inequalities of Paley, Hausdorff–Young, and Hardy–Littlewood and their relations. Finally, we also prove Pitt’s inequality for the Weyl transform.

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.