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  • Research Article
  • Open Access

Uniform Boundedness for Approximations of the Identity with Nondoubling Measures

Journal of Inequalities and Applications20072007:019574

https://doi.org/10.1155/2007/19574

  • Received: 15 May 2007
  • Accepted: 19 August 2007
  • Published:

Abstract

Let be a nonnegative Radon measure on which satisfies the growth condition that there exist constants and such that for all and , , where is the open ball centered at and having radius . In this paper, the authors establish the uniform boundedness for approximations of the identity introduced by Tolsa in the Hardy space and 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 that is bounded from to and is bounded from the local atomic Hardy space to . These results are proved to play key roles in establishing relations between and , BMO-type spaces RBMO and rbmo as well as RBLO and rblo , and also in characterizing rbmo and rblo .

Keywords

  • Growth Condition
  • Hardy Space
  • Maximal Operator
  • Open Ball
  • Radon Measure

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Authors’ Affiliations

(1)
School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

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