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This question is connected with my previous: Heisenberg group: function without vertical derivative. Here I am trying to look from another side: what is a difference between Sobolev space and ...

Let $\mathbb H$ be Heisenberg group with vector fields $$ X=\partial_x - \frac12y\partial_t,\quad Y=\partial_y + \frac12x\partial_t,\quad T=\partial_t $$ and $U\subset\mathbb H$ is an open set. I am ...