We prove basic properties of Orlicz-Morrey spaces and give a necessary and sufficient condition for boundedness of the Hardy-Littlewood maximal operator M from one Orlicz-Morrey space to another. For example, if f ∈ L(log L)(ℝⁿ), then Mf is in a (generalized) Morrey space (Example 5.1). As an application of boundedness of M, we prove the boundedness of generalized fractional integral operators, improving earlier results of the author.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm188-3-1,
author = {Eiichi Nakai},
title = {Orlicz-Morrey spaces and the Hardy-Littlewood maximal function},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {193-221},
zbl = {1163.46020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm188-3-1}
}
Eiichi Nakai. Orlicz-Morrey spaces and the Hardy-Littlewood maximal function. Studia Mathematica, Tome 187 (2008) pp. 193-221. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm188-3-1/