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Using double Bergman representation formula we provide new sharp estimates for distances from fixed analytic functions to some subspaces of holomorphic functions in unit polydisk and unit ball. We will enlarge the list of previously known assertions of this type obtained recently by R. Zhao and W. Xu.

SOME NEW ESTIMATES FOR DISTANCES IN ANALYTIC FUNCTION SPACES OF SEVERAL COMPLEX VARIABLES AND DOUBLE BERGMAN REPRESENTATION FORMULA