Necessary and sufficient conditions for the boundedness of the Riesz Potential in local Morrey-type spaces

Burenkov, Victor and Guliyev, V. S. 2009. Necessary and sufficient conditions for the boundedness of the Riesz Potential in local Morrey-type spaces. Potential Analysis 30 (3) , pp. 211-249. 10.1007/s11118-008-9113-5

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Abstract

The problem of the boundedness of the Riesz potential I α , 0 < α < n, in local Morrey-type spaces is reduced to the 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 the boundedness in local Morrey-type spaces for all admissible values of the parameters. Moreover, for a certain range of the parameters, these sufficient conditions coincide with the necessary ones.

Item Type:	Article
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Riesz potential, Fractional maximal operator, Local Morrey-type spaces, Hardy operator on the cone of monotonic functions, Weak Morrey-type spaces, Weighted estimates
Publisher:	Springer Netherlands
ISSN:	0926-2601
Last Modified:	04 Jun 2017 08:47
URI:	https://orca.cardiff.ac.uk/id/eprint/84904

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