EN
We define a class of spaces $H^{p}_{μ}$, 0 < p < ∞, of holomorphic functions on the tube, with a norm of Hardy type:
$||F||^{p}_{H^{p}_{μ}} = sup_{y∈Ω} ∫_{Ω̅} ∫_{ℝⁿ} |F(x+i(y+t))|^{p} dxdμ(t)$.
We allow μ to be any quasi-invariant measure with respect to a group acting simply transitively on the cone. We show the existence of boundary limits for functions in $H^{p}_{μ}$, and when p ≥ 1, characterize the boundary values as the functions in $L^{p}_{μ}$ satisfying the tangential CR equations. A careful description of the measures μ when their supports lie on the boundary of the cone is also provided.