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

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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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