Abstract
For smooth functions defined on a bounded domain satisfying the weak sigma-horn condition, integral representations in terms of their derivatives and their differences are introduced. These representations are employed to prove embedding theorems in the B-Pi,theta i(< ri >) (Omega)-function spaces, 1 <= p(i), theta(i) <= infinity, r(i) = (r(1)(i), r(2)(i),..., r(n)(i)) with r(j)(i) >= 0 for all i = 0, 1, 2, ... , n and j = 1, 2, ... , n.