Embedding Hardy spaces Hp into tent spaces and generalized integration operators

Let 0 < p, s < infinity, n be a nonnegative integer and mu be a positive Borel measure on D. Let T-s(p, n)(mu) be the space of all analytic functions f such that sup (I subset of partial derivative D) 1/vertical bar I vertical bar(s) integral(S(I)) vertical bar f((n)) (z) (1-vertical bar z vertical bar(2))(n)vertical bar(p) d mu(z) <infinity. In this paper, the boundedness and compactness of embedding from Hardy spaces H-p into T-s (p,n) (mu) are studied. As an application, the boundedness, compactness and essential norm of the generalized integral operators T-g(n,k) and S-g(n,0) acting from H-p to general function spaces are also investigated.