The problem of boundedness of the Hardy-Littewood maximal operator in local and global Morrey-type spaces is reduced to the problem of boundedness of the Hardy operator in weighted -spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for boundedness for all admissible values of the parameters. Moreover, in case of local Morrey-type spaces, for some values of the parameters, these sufficient conditions are also necessary.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-4,
author = {Viktor I. Burenkov and Huseyn V. Guliyev},
title = {Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {157-176},
zbl = {1044.42015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-4}
}
Viktor I. Burenkov; Huseyn V. Guliyev. Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces. Studia Mathematica, Tome 162 (2004) pp. 157-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-4/