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Uniform Boundedness for Approximations of the Identity with Nondoubling Measures
Journal of Inequalities and Applications volume 2007, Article number: 019574 (2007)
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.
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Yang, D., Yang, D. Uniform Boundedness for Approximations of the Identity with Nondoubling Measures. J Inequal Appl 2007, 019574 (2007). https://doi.org/10.1155/2007/19574
- Growth Condition
- Hardy Space
- Maximal Operator
- Open Ball
- Radon Measure