Characterizations for Besov spaces and applications. Part I

The main theorem of this paper gives a characterization for holomorphic Besov space Bp(D) over a large class of bounded domains D in Cn, which states that there is a bounded linear operator VD:Bp(D)→Lp(D,dλ) so that PVD=I on Bp(D), where P is the Bergman projection, and dλ(z)=K(z,z)dv is the biholomorphic invariant measure with K(z,z) being Bergman kernel function for D. Moreover, some application for characterizing Schatter von Neumann p-class small Hankel operation is given as a direct consequence of this theorem.