Local Morrey and Campanato Spaces on Quasimetric Measure Spaces. (25th May 2014)

• Record Type: Journal Article
• Authors: Stempak, Krzysztof; Tao, Xiangxing
• Other Names: Yang Dachun Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-05-25
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/172486
• Languages: English
• ISSNs: 2314-8896

Abstract

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 ofR n .