We prove that if q is in (1,\infty), Y is a Banach space and T is a linear
operator defined on the space of finite linear combinations of (1,q)-atoms in
R^n which is uniformly bounded on (1,q)-atoms, then T admits a unique
continuous extension to a bounded linear operator from H^1(R^n) to Y. We show
that the same is true if we replace (1,q)-atoms with continuous
(1,\infty)-atoms. This is known to be false for (1,\infty)-atoms.Comment: This paper will appear in Proceedings of the American Mathematical
Societ
