Embedding Derivatives and Integration Operators on Hardy Type Tent Spaces

In this paper, we completely characterize the positive Borel measures mu on the unit ball B-n such that the differential type operator R-m of order m is an element of N is bounded from Hardy type tent space HTq,alpha p (B-n) into L-s (mu) for full range of p, q, s, alpha. Subsequently, the corresponding compact description of differential type operator R-m is also characterized. As an application, we obtain the boundedness and compactness of integration operator J(g) from HTq,alpha p (B-n) to HTs,beta t (B-n), and the methods used here are adaptable to the Hardy spaces.