Extension domains for Hardy spaces

We show that a proper open subset Omega subset of R(n )is an extension domain for Hp (0 < p <= 1) if and only if it satisfies a certain geometric condition. When n(1/p - 1) is an element of N, this condition is equivalent to the global Markov condition for Omega (c), for p = 1 it is stronger, and when n(1/p - 1) is not an element of N U {0}, every proper open subset is an extension domain for H-p. We show that in each case a linear extension operator exists. We apply our results to study some complemented subspaces of BMO(R-n).