On some new projection theorems and sharp estimates in Herz type spaces in bounded pseudoconvex domains

We prove new projection theorems for new Herz type spaces in various domains $C_n$ in the unit disk, unit ball, bounded pseudoconvex domains and based on these results we provide sharp estimates for distances in such type spaces under one condition on Bergman kernel. Similar type result in such type spaces in tubular domains over symmetric cones will be also provided