Paraproducts and the exponential-square class

We prove that if a locally integrable f has a pointwise bounded dyadic square function, where the square function is defined with respect to a so-called “accretive” weight b, then f is locally exponentially square integrable. We generalize the result to d dimensions by means of “canonical” Haar functions for L2(Rd ).  2002 Elsevier Science (USA). All rights reserved