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arXiv · 2406.16731

On the boundedness of Dunkl multipliers

Suman Mukherjee·Sundaram Thangavelu
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Abstract

In this article we use Littlewood-Paley-Stein theory to prove two versions of Dunkl multiplier theorem when the multiplier $ m $ satisfies a modified H\"ormander condition. When $ m $ is radial we give a simple proof of a known result. For general $ m $ we prove that the Dunkl multiplier operator takes radial functions in $ L^p $ boundedly into $ L^p $ for all $ p \geq 2.$

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Suman Mukherjee, Sundaram Thangavelu. 2024-06-24. On the boundedness of Dunkl multipliers. https://doi.org/10.4064/sm240626-24-11

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