Geodesic
Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces
Viktor I. Burenkov1 ; Huseyn V. Guliyev1
1 School of Mathematics Cardiff University PO Box 926 Cardiff, CF24 4YH United Kingdom
Studia Mathematica, Tome 163 (2004) no. 2, pp. 157-176

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm163-2-4
Keywords: problem boundedness hardy littewood maximal operator local global morrey type spaces reduced problem boundedness hardy operator weighted p spaces cone non negative non increasing functions allows obtaining sufficient conditions boundedness admissible values parameters moreover local morrey type spaces values parameters these sufficient conditions necessary

Viktor I. Burenkov 1 ; Huseyn V. Guliyev 1

1 School of Mathematics Cardiff University PO Box 926 Cardiff, CF24 4YH United Kingdom 
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Viktor I. Burenkov; Huseyn V. Guliyev. Necessary and sufficient conditions for boundedness of
 the maximal operator in local Morrey-type spaces. Studia Mathematica, Tome 163 (2004) no. 2, pp. 157-176. doi: 10.4064/sm163-2-4

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