FATOU PROPERTY OF PREDUAL MORREY
SPACES WITH NON-DOUBLING MEASURES
Yoshihiro Sawano1, Hitoshi Tanaka2
1Department of Mathematics and Information Sciences
Tokyo Metropolitan University
1-1 Minami Ohsawa, Hachioji, Tokyo 192-0397, JAPAN
2Graduate School of Mathematical Sciences
The University of Tokyo
Tokyo, 153-8914, JAPAN
Abstract. The aim of this paper is to establish that the predual Morrey spaces are closed under taking increasing limit. As an application, the boundedness property of the fractional integral operators on predual Morrey spaces is obtained. This result answers the (open) question from our earlier paper ``Predual spaces of Morrey spaces with non-doubling measures''. This property will be used to supplement that paper, where the boundedness property of the fractional integral operators is missing.
AMS Subject classification: 42B25, 26A33
Keywords and phrases: Morrey space, non-doubling measure, predual space


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DOI: 10.12732/ijam.v27i3.8

Volume: 27
Issue: 3
Year: 2014