Tent Carleson measures and superposition operators on Hardy type tent spaces

In this paper, we completely characterize the positive Borel measures μ on the unit ball Bₙ of Cⁿ such that the Carleson embedding from holomorphic Hardy type tent spaces HTᵖq,α into the tent spaces Tᵗₛ(μ) is bounded for all 0<p,q,s,t<∞ and α>-n-1. As an application, we determine the indices 0<p,q,s,t<∞ and α,β>-n-1 such that the inclusion HTᵖq,αᵗs,β holds, which allows us to completely characterize the nonlinear superposition operators between Hardy type tent spaces.