Affiliation:
1. Department of Mathematics , [ 28817]Indian Institute of Technology Delhi, Delhi – 110016 , India
Abstract
Abstract
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}}
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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.