Burenkov, Viktor I.; Guliyev, Huseyn V. Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces. (English) Zbl 1044.42015 Stud. Math. 163, No. 2, 157-176 (2004). Summary: 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. Cited in 2 ReviewsCited in 94 Documents MSC: 42B25 Maximal functions, Littlewood-Paley theory 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:boundedness; Hardy-Littewood maximal operator; Morrey-type spaces; Hardy operator PDFBibTeX XMLCite \textit{V. I. Burenkov} and \textit{H. V. Guliyev}, Stud. Math. 163, No. 2, 157--176 (2004; Zbl 1044.42015) Full Text: DOI Link