Correction to “hardy and Bmo Spaces Associated to Divergence Form Elliptic Operators” Steve Hofmann and Svitlana Mayboroda

We present here a correction to an error in our paper [5]. We are grateful to Dachun Yang for bringing the error to our attention, and we thank Alan McIntosh for helpful discussions which have led to this correction of the error. In particular, our approach here follows that of Auscher, McIntosh and Russ [1], as explained to us by McIntosh. In [5] we develop a theory of H1 (Hardy type) and BMO spaces adapted to a second order, divergence form elliptic (aka accretive) operator L in Rn, with complex, L coefficents. This had been done previously in work of Duong and Yan [2, 3], assuming a pointwise Gaussian bound on the heat kernel associated to L, which need not hold for arbitrary operators of the type that we consider. The point of our work, then, was to develop a theory analogous to that of [2, 3], in the absence of the Gaussian assumption. In particular we establish the equivalence of several different H1 type spaces, based on membership in L1 of various square functions and non-tangential maximal functions adapted to L (if L is the Laplacian, then this theory reduces to that of the classical Hardy and BMO spaces). Among these (and of central importance) is the “square function Hardy space” H1 S h , defined as the completion of the set