The problem of boundedness of the Riesz potential in local Morreytype 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 sharp sufficient conditions for boundedness for all admissible values The research of V. Burenkov was partially supported by the grants of the RFBR (project 09-01-00093a) and 68 V.I. Burenkov et al.of the parameters, which, for a certain range of the parameters wider than known before, coincide with the necessary ones.Keywords Riesz potential · Local and global Morrey-type spaces · Hardy operator on the cone of monotonic functions Mathematics Subject Classifications (2010) Primary 42B20 · 42B25 · 42B35
In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.
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