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Journal of Function Spaces
Volume 2014, Article ID 172486, 15 pages
http://dx.doi.org/10.1155/2014/172486
Research Article

Local Morrey and Campanato Spaces on Quasimetric Measure Spaces

1Instytut Matematyki i Informatyki, Politechnika Wrocławska, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
2Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, China

Received 17 February 2014; Accepted 15 April 2014; Published 25 May 2014

Academic Editor: Dachun Yang

Copyright © 2014 Krzysztof Stempak and Xiangxing Tao. 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

We define and investigate generalized local Morrey spaces and generalized local Campanato spaces, within a context of a general quasimetric measure space. The locality is manifested here by a restriction to a subfamily of involved balls. The structural properties of these spaces and the maximal operators associated to them are studied. In numerous remarks, we relate the developed theory, mostly in the “global” case, to the cases existing in the literature. We also suggest a coherent theory of generalized Morrey and Campanato spaces on open proper subsets of .