"Paley inequality for the Weyl transform and its applications"Singhal, RitikaOur aim is to prove the classical Paley inequality in the context of the Weyl transform. As the Weyl transform maps function spaces to bounded operator, we could prove several versions of this inequality. As for some applications, we prove a version of the H\"ormander's multiplier theorem to discuss $L^p$-$L^q$ boundedness of the Weyl multipliers and prove the Hardy-Littlewood inequality. We also consider the vector-valued version of the Paley inequality to eventually prove the Pitt's inequality for the Weyl transform. |
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