Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 9 (2011), Issue 3, Pages 245-282
http://dx.doi.org/10.1155/2011/187597

Boundedness of Lusin-area and gλ* functions on localized Morrey-Campanato spaces over doubling metric measure spaces

1College of Science, China Agricultural University Beijing 100083, China
2School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
3Department of Mathematics, Osaka Kyoiku University Kashiwara, Osaka 582-8582, Japan
4Department of Mathematics, Ibaraki University Mito Ibaraki 310-5812, Japan
5School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received 1 June 2009

Academic Editor: Fernando Cobos

Copyright © 2011 Hindawi Publishing Corporation. 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.

Abstract

Let χ be a doubling metric measure space and ρ an admissible function on χ. In this paper, the authors establish some equivalent characterizations for the localized Morrey-Campanato spaces ερα,p(χ) and Morrey-Campanato-BLO spaces ε̃ρα,p(χ) when α(-,0) and p[1,). If χ has the volume regularity Property (P), 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 ερa,p(χ) to ε̃ρa,p(χ) without invoking any regularity of considered kernels. The same is true for the gλ* function and, unlike the Lusin-area function, in this case, χ is even not necessary to have Property (P). These results are also new even for d with the d-dimensional Lebesgue measure and have a wide applications.