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

Burenkov, Victor and Guliyev, H. V. 2004. Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces. Studia Mathematica 163 (2) , pp. 157-176. 10.4064/sm163-2-4

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Abstract

It is proved that the boundedness of the maximal operator M from a Lebesgue space L-p1 (R-n) to a general local Morrey-type space LMp2 theta,w(R-n) is equivalent to the boundedness of the embedding operator from L-p1(R-n) to LMp2 theta,(w)(R-n) and in its turn to the boundedness of the Hardy operator from L-p1/p2 (0,infinity) to the weighted Lebesgue space L-theta/p2,L-v (0,infinity) for a certain weight function v determined by the functional parameter w. This allows obtaining necessary and sufficient conditions on the function w ensuring the boundedness of M from L-p1 (R-n) to LMp2 theta,w(R-n) for any 0< theta <= infinity, 0< p(2) <= p(1) <= infinity, p(1) > 1. These conditions with p(1) = p(2) = 1 are necessary and sufficient for the boundedness of M from L-1(R-n) to the weak local Morreytype space WLM1 theta,w(R-n).

Item Type:	Article
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Inequalities.
Publisher:	Institute of Mathematics of the Polish Academy of Sciences
ISSN:	0039-3223
Last Modified:	04 Jun 2017 08:47
URI:	https://orca.cardiff.ac.uk/id/eprint/84917

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