  The ``asymmetric'' matrix element <p-r|G...G|p> that appears in the pQCD
description of hard diffractive electroproduction does not coincide with that
defining the gluon distribution function f_g(x). I outline a pQCD formalism
based on a concept of the double distribution F_g(x,y), which specifies the
fractions xp, yr, (1-y)r of the initial proton momentum p and the momentum
transfer r, resp., carried by the gluons. For $t \equiv r^2 =0$, r is
proportional to p: $r = \zeta p$, and it is convenient to parameterize the
matrix element <p-r|G...G|p> by an asymmetric distribution function ${\cal
F}_{\zeta}^g (X)$ depending on the total fractions $X \equiv x+y \zeta$ and
$X-\zeta = x- (1-y) \zeta$ of the initial hadron momentum p carried by the
gluons.I formulate evolution equations for ${\cal F}_{\zeta}^g (X)$, study some
of their general properties and discuss the relationship between ${\cal
F}_{\zeta}^g (X)$, F_g(x,y) and f_g(x).
