An extension problem, trace Hardy and Hardy's inequalities for Ornstein-Uhlenbeck operator

Pritam Ganguly, Ramesh Manna, Sundaram Thangavelu

In this paper, we study an extension problem for the Ornstein-Uhlenbeck operator $L=-\Delta +2x\cdot \nabla +n$ and we obtain various characterisations of the solution of the same. We use…