Intersection properties of weak analytically uniform classes of functions

1. The notation is standard. N, Z, R, R +, C denote respectively the natural, integral, real, real positive, and complex numbers. Re ~ and Im ~ is the real and the imaginary part of ~EC". [1 is the usual norm in C". By g(t), tER + u {+ oo}, we denote the C = functions defined for Ix[<t, xER", and by Co(t ) the C ~ functions with support in IxI<t. g(t) is endowed with the usual topology. If I" is a linear topological space, then X' stands for its dual. The Fourier--Borel transform of u E d ' (C") is denoted t~ or flu. Further, g ' [B], B < t is defined by 8 ' [B] = ={uEg'(t); supp u c {Ixt <B}}. Finally, 0 denotes the Cauchy--Riemann operator, and, for a multi-index ~, D" is the corresponding derivation.