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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