Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

Let s is an element of R, p is an element of (0, 1] and q is an element of [p, infinity). It is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from the Triebel-Lizorkin space (F)over dot(p,q)(s)(R-n) to a quasi-Banach space B if and only if sup{parallel to T(a)parallel to B : a is an infinitely differentiable (p,q,s)-atom (F)over dot(p,q)(s)(R-n)} < infinity where the (p, q, s)-atom of (F)over dot(p,q)(s)(R-n) is as defined by Han, Paluszynski and Weiss.