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

Viktor I. Burenkov; Huseyn V. Guliyev

Studia Mathematica (2004)

  • Volume: 163, Issue: 2, page 157-176
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Viktor I. Burenkov, and Huseyn V. Guliyev. "Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces." Studia Mathematica 163.2 (2004): 157-176. <http://eudml.org/doc/284394>.

@article{ViktorI2004,
abstract = {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.},
author = {Viktor I. Burenkov, Huseyn V. Guliyev},
journal = {Studia Mathematica},
keywords = {boundedness; Hardy-Littewood maximal operator; Morrey-type spaces; Hardy operator},
language = {eng},
number = {2},
pages = {157-176},
title = {Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces},
url = {http://eudml.org/doc/284394},
volume = {163},
year = {2004},
}

TY - JOUR
AU - Viktor I. Burenkov
AU - Huseyn V. Guliyev
TI - Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces
JO - Studia Mathematica
PY - 2004
VL - 163
IS - 2
SP - 157
EP - 176
AB - 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.
LA - eng
KW - boundedness; Hardy-Littewood maximal operator; Morrey-type spaces; Hardy operator
UR - http://eudml.org/doc/284394
ER -

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