TY - JOUR AU - Yang, Dachun AU - Yang, Dongyong PY - 2007 DA - 2007/10/16 TI - Uniform Boundedness for Approximations of the Identity with Nondoubling Measures JO - Journal of Inequalities and Applications SP - 019574 VL - 2007 IS - 1 AB - Letbe a nonnegative Radon measure onwhich satisfies the growth condition that there exist constantsandsuch that for alland,, whereis the open ball centered atand having radius. In this paper, the authors establish the uniform boundedness for approximations of the identity introduced by Tolsa in the Hardy spaceand the BLO-type space RBLO. Moreover, the authors also introduce maximal operators(homogeneous) and(inhomogeneous) associated with a given approximation of the identity, and prove thatis bounded fromtoandis bounded from the local atomic Hardy spaceto. These results are proved to play key roles in establishing relations betweenand, BMO-type spaces RBMOand rbmoas well as RBLOand rblo, and also in characterizing rbmoand rblo. SN - 1029-242X UR - https://doi.org/10.1155/2007/19574 DO - 10.1155/2007/19574 ID - Yang2007 ER -