Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of Cn

Abstract EN

We obtain weighted integral representations for spaces of functions holomorphic in the unit ball Bn and belonging to area-integrable weighted Lp-classes with “anisotropic” weight function of the type ∏i=1n(1−|w1|2−|w2|2−⋯−|wi|2)αi, w=(w1,w2,…,wn)∈Bn.

The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for n=2).