We obtain sufficient conditions and necessary conditions for the maximal operator to be bounded in the generalized grand Lebesgue space on an open set Ω ∈ Rn which is not necessarily bounded. The sufficient conditions coincide with necessary conditions for instance in the case where Ω is bounded and the standard definition of the grand space is used.
Hardy-Littlewood maximal operator in generalized grand Lebesgue spaces
10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 ; 2014 ; Narvik, Norway
AIP Conference Proceedings ; 1637 , 1 ; 1137-1142
2014-12-10
6 pages
Conference paper
Electronic Resource
English
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