Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Uniform Boundedness for Approximations of the Identity with Nondoubling Measures Dachun Yang and Dongyong Yang | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 19574 25 pages doi 2007 19574 Research Article Uniform Boundedness for Approximations of the Identity with Nondoubling Measures Dachun Yang and Dongyong Yang Received 15 May 2007 Accepted 19 August 2007 Recommended by Shusen Ding Let p be a nonnegative Radon measure on Rd which satisfies the growth condition that there exist constants c0 0 and n e 0 d such that for all x e Rd and r 0 p B x r c0rn where B x r is the open ball centered at x and having radius r. In this paper the authors establish the uniform boundedness for approximations of the identity introduced by Tolsa in the Hardy space H 1 p and the BLO-type space RBLO p . Moreover the authors also introduce maximal operators Ms homogeneous and Ms inhomogeneous associated with a given approximation of the identity s and prove that Ms is bounded from H1 p to L1 p and Ms is bounded from the local atomic Hardy space fi tb p to L1 p . These results are proved to play key roles in establishing relations between H 1 p and hitb p BMO-type spaces RBMO p and rbmo p as well as RBLO p and rblo p and also in characterizing rbmo p and rblo p . Copyright 2007 D. Yang and D. Yang. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Recall that a nondoubling measure p on Rd means that p is a nonnegative Radon measure which only satisfies the following growth condition namely there exist constants c0 0 and n e 0 d such that for all x e Rd and r 0 p B x r C0rn where B x r is the open ball centered at x and having radius r. Such a measure p is not necessary to be doubling which is a key assumption in the classical theory of harmonic analysis. In recent years it was shown that many results on the Calderon-Zygmund theory 2 Journal of Inequalities and .
