The Journal of Fourier Analysis and Applications presents papers that treat mathematical analysis and its numerous applications and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Wilson’s paper is available electronically on SpringerLink:
http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00041-010-9165-y[1]
For more information on this research contact: wilson@cems.uvm.edu
Abstract
We prove that a general form of the Calderón reproducing formula converges in H1(Rd ) (the real Hardy space of Fefferman and Stein) as a natural limit of approximating integrals. We show that this convergence is H1-stable with respect to small errors in dilation and translation. Using duality, we show that the Calderón reproducing formula converges, in a stable fashion, weak-∗ in BMO. We give quantitative estimates of the formula’s stability and rate of convergence. These theorems generalize results of the author on the convergence and stability of the Calderón reproducing formula in Lp(w), where 1<p<∞and w is a Muckenhoupt Ap weight.