Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Ministry of Education, Beijing 100875, China
Copyright © 2009 Qingying Xue and Juyang Zhang. 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.
Let be a positive Radon measure on which may be nondoubling. The only condition that satisfies is for all , , and some fixed constant . In this paper, we introduce the operator related to such a measure and assume it is bounded on . We then establish its boundedness, respectively,
from the Lebesgue space to the weak Lebesgue space , from the Hardy
space to and from the Lesesgue space to the space . As a corollary, we obtain the boundedness of in the Lebesgue space with .