Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces
Tom 163 / 2004
Studia Mathematica 163 (2004), 157-176
MSC: Primary 42B25.
DOI: 10.4064/sm163-2-4
Streszczenie
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 $L_p$-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.
