Weighted Young-type inequalities on locally compact groups

Frédéric Morneau-Guérin

We obtain an extension of Young's convolution inequality in weighted Lebesgue spaces of measurable functions defined on locally compact groups. Our result provides a unified treatment of a theorem of Klein and Russo extending the classical Young's inequality to locally compact groups, and a theorem of Biswas and Swanson generalizing Young's inequality to weighted Lebesgue spaces on locally compact Abelian groups.