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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The research of V. Burenkov was partially supported by the grants of the RFBR (project 09-01-00093a) and DGF-RFBR (project 10-01-91331). The research of A. Gogatishvili was partially supported by the grants no. 201/05/2033 and 201/08/0383 of the Grant Agency of the Czech Republic and by the Institutional Research Plan no. AV0Z10190503 of AS CR. The research of V. Guliyev was partially supported by the grant of 2010-Ahi Evran University Scientific Research Projects (BAP FBA-10-05). The research of V. Guliyev and R. Mustafayev was partially supported by the grant of BGP II (project ANSF Award/AZM1-3110-BA-08). The research of R. Mustafayev was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan no. AV0Z10190503 and by a Post Doctoral Fellowship of INTAS (Grant 06-1000015-6385).
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Burenkov, V.I., Gogatishvili, A., Guliyev, V.S. et al. Boundedness of the Riesz Potential in Local Morrey-Type Spaces. Potential Anal 35, 67–87 (2011). https://doi.org/10.1007/s11118-010-9205-x
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DOI: https://doi.org/10.1007/s11118-010-9205-x