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Necessary and Sufficient Conditions for the Boundedness of the Riesz Potential in Local Morrey-type Spaces

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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.

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Authors and Affiliations

  1. Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK

    Victor I. Burenkov

  2. Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku State University, F. Agayev St. 9, Baku, AZ 1141, Azerbaijan

    Vagif S. Guliyev

Authors
  1. Victor I. Burenkov
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  2. Vagif S. Guliyev
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Corresponding author

Correspondence to Vagif S. Guliyev.

Additional information

V. Burenkov’s research was partially supported by the grant of the Russian Foundation for Basic Research (Grant 06-01-00341).

V. Burenkov’s and V. Guliyev’s research was partially supported by the grant of INTAS (project 05-1000008-8157).

V. Guliyev’s research was partially supported by the grant of the Azerbaijan-U. S. Bilateral Grants Program II (project ANSF Award / AZM1-3110-BA-08) and the Turkish Scientific and Technological Research Council (TUBITAK, programme 2221, no. 220.01-619-4889).

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Burenkov, V.I., Guliyev, V.S. Necessary and Sufficient Conditions for the Boundedness of the Riesz Potential in Local Morrey-type Spaces. Potential Anal 30, 211–249 (2009). https://doi.org/10.1007/s11118-008-9113-5

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