Alexander Meskhi (Scuola Normale Superiore di Pisa)
Fractional integrals on nonhomogeneous spaces
Abstract.
Necessary and sufficient conditions on a measure governing two-weight inequalities for potential operators defined on nonhomogeneous spaces are established, where the weights are of power type. Theorems of Sobolev and Adams type for fractional integrals on measure spaces will be also discussed.
The talk is based on the monograph D. E. Edmunds, V. Kokilashvili and A. Meskhi, Bounded and Compact Integral Operators Kluwer Academic Publishers, Dordrecht, Boston, London}, 2002, and the paper V. Kokilashvili and A. Meskhi, On some weighted inequalities for fractional integrals on nonhomogeneous spaces (to appear).

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