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Criteria for the boundedness and compactness of generalized one-sided potentials. (English) Zbl 1018.42011

Necessary and sufficient conditions are obtained for the positive Borel measure \(\nu\) which provide the boundedness/compactness of certain Riemann-Liouville type operators in Lebesgue spaces endowed with the measure \(\nu\).

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
47G10 Integral operators
26A33 Fractional derivatives and integrals
47B38 Linear operators on function spaces (general)
46E40 Spaces of vector- and operator-valued functions
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