Boundedness of the Riesz Potential in Local Morrey-Type Spaces |
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| Authors: | Victor I. Burenkov Amiran Gogatishvili Vagif S. Guliyev Rza Ch. Mustafayev |
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| Affiliation: | 1.Dipartimento di matematica pura ed applicata,Padova University,Padova,Italy;2.Institute of Mathematics of the Academy of Sciences of the Czech Republic,Prague 1,Czech Republic;3.Department of Mathematics,Ahi Evran University,Kirsehir,Turkey;4.Institute of Mathematics and Mechanics,Academy of Sciences of Azerbaijan,Baku,Azerbaijan |
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| Abstract: | The problem of boundedness of the Riesz potential in local Morrey-type 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 of the parameters, which, for a certain range of the parameters wider than known before, coincide with the necessary ones. |
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