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.
Wilson, J. M. (2002). Paraproducts and the exponential-square class. Journal of Mathematical Analysis and Applications, 271(2), 374–382. https://doi.org/10.1016/S0022-247X(02)00121-X