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Morrey spaces and fractional integral operators. (English) Zbl 1181.26014
The aim of this paper is to establish the boundedness of fractional integral operators in Morrey spaces defined on quasimetric measure spaces. The author also derives Sobolev-, trace- and two-weight-inequalities for fractional integrals. In the case that the measure satisfies the doubling condition, the derived conditions are necessary and sufficient for appropriate inequalities.
MSC:
26A33Fractional derivatives and integrals (real functions)
42B35Function spaces arising in harmonic analysis
47B38Operators on function spaces (general)
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