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On the boundedness of Dunkl multipliers (2406.16731v2)

Published 24 Jun 2024 in math.FA and math.CA

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 $ Lp $ boundedly into $ Lp $ for all $ p \geq 2.$

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