Necessary and sufficient conditions for the boundedness of fractional maximal operators in local Morrey-type spaces.

Burenkov, Victor, Guliyev, Huseyn V. and Guliyev, Vagif S. 2007. Necessary and sufficient conditions for the boundedness of fractional maximal operators in local Morrey-type spaces. Journal of Computational and Applied Mathematics 208 (1) , pp. 280-301. 10.1016/j.cam.2006.10.085

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Abstract

The problem of the boundedness of the fractional maximal operator Mα, 0<α<n, in local and global Morrey-type spaces is reduced to the problem of the boundedness of the Hardy operator in weighted Lp-spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for the 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 coincide with the necessary ones.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Maximal operator ; Fractional maximal operator ; Local and global Morrey-type spaces ; Weak Morrey-type spaces ; Hardy operator on the cone of monotonic functions
Publisher:	Elsevier
ISSN:	03770427
Last Modified:	04 Jun 2017 01:41
URI:	https://orca.cardiff.ac.uk/id/eprint/1682

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