Embedding Derivatives and Integration Operators on Hardy Type Tent Spaces.

In this paper, we completely characterize the positive Borel measures μ on the unit ball B n such that the differential type operator ℛ m of order m ∈ ℕ is bounded from Hardy type tent space ℋ T q , α p (B n) into L^s(μ) for full range of p, q, s, α. 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 ℋ T q , α p (B n) to ℋ T s , β t (B n) , and the methods used here are adaptable to the Hardy spaces. [ABSTRACT FROM AUTHOR]