Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

Streszczenie

We define a class of spaces $H^p_\mu$, $0< p< \infty$, of holomorphic functions on the tube, with a norm of Hardy type: $$\|F\|^p_{H^p_\mu}= \sup_{y\in{\mit\Omega}}\int_{{\overline{{\mit\Omega}}}}\int_{{\mathbb R}^n} |F(x+i(y+t))|^p\,dx\,d\mu(t). $$ We allow $\mu$ 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 $H^p_\mu$, and when $p\geq1$, characterize the boundary values as the functions in $L^p_\mu$ satisfying the tangential CR equations. A careful description of the measures $\mu$ when their supports lie on the boundary of the cone is also provided.