Haibo Lin, Eiichi Nakai, Dachun Yang, "Boundedness of Lusin-area and functions on localized Morrey-Campanato spaces over doubling metric measure spaces", Journal of Function Spaces, vol. 9, Article ID 187597, 38 pages, 2011. https://doi.org/10.1155/2011/187597
Boundedness of Lusin-area and functions on localized Morrey-Campanato spaces over doubling metric measure spaces
Let be a doubling metric measure space and an admissible function on . In this paper, the authors establish some equivalent characterizations for the localized Morrey-Campanato spaces and Morrey-Campanato-BLO spaces when and . If has the volume regularity Property , the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the semigroup generated by the Schrödinger operator, from to without invoking any regularity of considered kernels. The same is true for the function and, unlike the Lusin-area function, in this case, is even not necessary to have Property . These results are also new even for with the -dimensional Lebesgue measure and have a wide applications.
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