Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of C n

Abstract

We obtain weighted integral representations for spaces of functions holomorphic in the unit ball $B_n$ and belonging to area-integrable weighted $L^p$-classes with “anisotropic” weight function of the type ${{\displaystyle \prod }}_{i=1}^n{(1-|w_1{|}^2-|w_2{|}^2-\cdots -|w_i{|}^2)}^{{\alpha }_i}$, $w=(w_1,w_2,\dots ,w_n)\in B_n$. The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for $n=2$).