Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces

Tom 163 / 2004

Viktor I. Burenkov, Huseyn V. Guliyev 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.

Autorzy

  • Viktor I. BurenkovSchool of Mathematics
    Cardiff University
    PO Box 926
    Cardiff, CF24 4YH
    United Kingdom
    e-mail
  • Huseyn V. GuliyevSchool of Mathematics
    Cardiff University
    PO Box 926
    Cardiff, CF24 4YH
    United Kingdom
    e-mail

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