On Hardy type spaces in some domains in $\mathbb{C}^n$ and related problems

We discuss some new problems in several new mixed norm Hardy type spaces in products of bounded pseudoconvex domains with smooth boundary in $\mathbb{C}^n$ and then prove some new sharp decomposition theorems for multifunctional Hardy type spaces in the unit ball and then we show also similar results in pseudoconvex and convex domains of finite type extending previously known assertions obtained by first author earlier in Bergman spaces under certain Poisson integral type condition which vanishes in one functional case. Some new (in particular sharp in the unit ball) embeddings for some new mixed norm Hardy spaces in bounded pseudoconvex domains will be also indicated. Some new extensions of Poisson integral in the unit ball and some new assertions concerning them will be indicated and discussed in product domains. Some related multifunctional results are also given. Some new embedding theorems are also provided in some new mixed norm Hardy spaces in $\mathbb{C}^n$ unbounded tubular domains over symmetric cones.